subject:(Dynamical systems)

1. Carter, Paul A. Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System.

Degree: PhD, Mathematics, 2016, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:674229/

► The FitzHugh-Nagumo equations are known to admit fast traveling pulses that have monotone tails and arise as the concatenation of Nagumo fronts and backs in… (more)

Subjects/Keywords: dynamical systems

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APA (6^th Edition):

Carter, P. A. (2016). Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:674229/

Chicago Manual of Style (16^th Edition):

Carter, Paul A. “Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System.” 2016. Doctoral Dissertation, Brown University. Accessed February 22, 2020. https://repository.library.brown.edu/studio/item/bdr:674229/.

MLA Handbook (7^th Edition):

Carter, Paul A. “Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System.” 2016. Web. 22 Feb 2020.

Vancouver:

Carter PA. Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System. [Internet] [Doctoral dissertation]. Brown University; 2016. [cited 2020 Feb 22]. Available from: https://repository.library.brown.edu/studio/item/bdr:674229/.

Council of Science Editors:

Carter PA. Fast Pulses with Oscillatory Tails in the FitzHugh-Nagumo System. [Doctoral Dissertation]. Brown University; 2016. Available from: https://repository.library.brown.edu/studio/item/bdr:674229/

2. Yi, Ren. Domain Exchange Transformations and Their Renormalizations.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792737/

► Domain exchange transformations (DETs) are dynamical systems of piecewise translations defined on piecewise smooth Jordan domains. DETs are two-dimensional generalizations of interval exchange transformations which… (more)

▼ Domain exchange transformations (DETs) are dynamical systems of piecewise translations defined on piecewise smooth Jordan domains. DETs are two-dimensional generalizations of interval exchange transformations which have been fruitfully-studied for more than 40 years. For DETs, renormalizations are the key to describe complete dynamical behaviors. We say that a DET is renormalizable if there is a subdomain to which the first return map is conjugate to the DET itself by an affine map. In this thesis, we study DETs arising from two general constructions and their renormalizations. Polygon exchange transformations (PETs) are DETs defined on polygonal domains with partitions into subpolygons. One general method of constructing PETs based on multigraphs was introduced by R. Schwartz in 2013. The resulting dynamical systems are called the multigraph PETs. In the first part of this thesis, we describe a 1-parameter family of multigraph PETs called the triple lattice PETs. We show that there exists a renormalization scheme of the triple lattice PETs in the parameter space (0, 1). By the renormalization scheme, we are able to analyze the limit set Λ when the parameter is the golden ratio. We show that Λ is the nested intersection of a countable sequence of finite unions of isosceles trapezoids and its Hausdorff dimension is 1.83157… which is less than 2. In the second part of this thesis, we explain how to use cut-and-and project set to construct minimal DETs. Specializing to the case when the domain is a unit square and the cut-and-project set is associated to a Galois lattice, we construct an infinite family of RETs (DETs on the unit square partitioned into rectilinear polygons). Each RET in the family is called a PV RET since every map is associated to a PV number. We prove that all PV RETs in the family are renormalizable. Moreover, we discover that certain PV RETs can be composed to create a new RET with the same combinatorics as any PV RET. The composition is called an admissible RET. We find a family of admissible RETs, called multistage RETs, which are renormalizable. This is a joint work with Ian Alevy and Richard Kenyon. Advisors/Committee Members: Schwartz, Richard (Advisor), Kenyon, Richard (Reader), Brock, Jeffrey (Reader).

Subjects/Keywords: dynamical systems

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APA (6^th Edition):

Yi, R. (2018). Domain Exchange Transformations and Their Renormalizations. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792737/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yi, Ren. “Domain Exchange Transformations and Their Renormalizations.” 2018. Thesis, Brown University. Accessed February 22, 2020. https://repository.library.brown.edu/studio/item/bdr:792737/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yi, Ren. “Domain Exchange Transformations and Their Renormalizations.” 2018. Web. 22 Feb 2020.

Vancouver:

Yi R. Domain Exchange Transformations and Their Renormalizations. [Internet] [Thesis]. Brown University; 2018. [cited 2020 Feb 22]. Available from: https://repository.library.brown.edu/studio/item/bdr:792737/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yi R. Domain Exchange Transformations and Their Renormalizations. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792737/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Makrides, Elizabeth. Existence and Stability of Spatially Localized Planar Patterns.

Degree: PhD, Applied Mathematics, 2015, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:674167/

► Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been… (more)

▼ Spatially localized structures, in which a spatially oscillatory pattern on a finite spatial range connects to a trivial homogeneous solution outside this range, have been observed in numerous physical contexts, including cellular buckling, plane Couette flow, vegetation patterns, optical cavity solitons, crime hotspots, and many others. Despite the widely disparate contexts in which they arise, the bifurcation diagrams of such patterns often exhibit similar snaking behavior, in which branches of symmetric solutions, connected by bifurcating branches of asymmetric solutions, wind back and forth between two limits of an appropriate parameter. In this thesis we address the existence and stability of stationary localized solutions of parabolic partial differential equations (PDEs) on the line and the plane. One particular model system supporting localized structures is the Swift – Hohenberg system, and we use this system for numerical illustration of our existence and stability results. Our main results are as follows: we give a new proof of the existence asymmetric localized structures, utilizing information about the underlying front structure and providing a unified approach to the existence of all localized structures. This enables a rigorous proof of the stability properties of symmetric and asymmetric structures. We show that the temporal eigenvalues of localized structures in the right half plane are exponentially close to those of the front and back added with multiplicity, and furthermore that the eigenvalue at the origin remains simple. We then address numerical results showing unexpected behavior of eigenvalues within the essential (or absolute) spectrum, and propose an analytical explanation of these results. We conclude by predicting the results of perturbative terms in PDE systems supporting localized snaking solutions, and make qualitative and quantitative predictions for topological changes to the associated bifurcation diagrams, as well as drift speeds of particular solutions. Advisors/Committee Members: Sandstede, Bjorn (Director), Beck, Margaret (Reader), Menon, Govind (Reader).

Subjects/Keywords: dynamical systems

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APA (6^th Edition):

Makrides, E. (2015). Existence and Stability of Spatially Localized Planar Patterns. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:674167/

Chicago Manual of Style (16^th Edition):

Makrides, Elizabeth. “Existence and Stability of Spatially Localized Planar Patterns.” 2015. Doctoral Dissertation, Brown University. Accessed February 22, 2020. https://repository.library.brown.edu/studio/item/bdr:674167/.

MLA Handbook (7^th Edition):

Makrides, Elizabeth. “Existence and Stability of Spatially Localized Planar Patterns.” 2015. Web. 22 Feb 2020.

Vancouver:

Makrides E. Existence and Stability of Spatially Localized Planar Patterns. [Internet] [Doctoral dissertation]. Brown University; 2015. [cited 2020 Feb 22]. Available from: https://repository.library.brown.edu/studio/item/bdr:674167/.

Council of Science Editors:

Makrides E. Existence and Stability of Spatially Localized Planar Patterns. [Doctoral Dissertation]. Brown University; 2015. Available from: https://repository.library.brown.edu/studio/item/bdr:674167/

4. McQuighan, Kelly Teresa. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.

Degree: PhD, Applied Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386200/

► Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can… (more)

Subjects/Keywords: dynamical systems

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APA (6^th Edition):

McQuighan, K. T. (2014). Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386200/

Chicago Manual of Style (16^th Edition):

McQuighan, Kelly Teresa. “Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.” 2014. Doctoral Dissertation, Brown University. Accessed February 22, 2020. https://repository.library.brown.edu/studio/item/bdr:386200/.

MLA Handbook (7^th Edition):

McQuighan, Kelly Teresa. “Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.” 2014. Web. 22 Feb 2020.

Vancouver:

McQuighan KT. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2020 Feb 22]. Available from: https://repository.library.brown.edu/studio/item/bdr:386200/.

Council of Science Editors:

McQuighan KT. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386200/

University of Minnesota

5. Leifeld, Juliann. Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model.

Degree: PhD, Mathematics, 2016, University of Minnesota

URL: http://hdl.handle.net/11299/182310

► Welander's model is a conceptual ocean convection model, that describes ocean convection with a few, simple dynamical equations. Welander's goal in formulating his model was… (more)

Subjects/Keywords: Dynamical Systems; Nonsmooth

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APA (6^th Edition):

Leifeld, J. (2016). Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/182310

Chicago Manual of Style (16^th Edition):

Leifeld, Juliann. “Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model.” 2016. Doctoral Dissertation, University of Minnesota. Accessed February 22, 2020. http://hdl.handle.net/11299/182310.

MLA Handbook (7^th Edition):

Leifeld, Juliann. “Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model.” 2016. Web. 22 Feb 2020.

Vancouver:

Leifeld J. Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model. [Internet] [Doctoral dissertation]. University of Minnesota; 2016. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/11299/182310.

Council of Science Editors:

Leifeld J. Smooth and Nonsmooth Bifurcations in Welander's Ocean Convection Model. [Doctoral Dissertation]. University of Minnesota; 2016. Available from: http://hdl.handle.net/11299/182310

University of North Texas

6. Ziegler, Caleb. On Factors of Rank One Subshifts.

Degree: 2018, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc1157623/

► Rank one subshifts are dynamical systems generated by a regular combinatorial process based on sequences of positive integers called the cut and spacer parameters. Despite… (more)

Subjects/Keywords: Mathematics; Dynamical Systems

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APA (6^th Edition):

Ziegler, C. (2018). On Factors of Rank One Subshifts. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc1157623/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ziegler, Caleb. “On Factors of Rank One Subshifts.” 2018. Thesis, University of North Texas. Accessed February 22, 2020. https://digital.library.unt.edu/ark:/67531/metadc1157623/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ziegler, Caleb. “On Factors of Rank One Subshifts.” 2018. Web. 22 Feb 2020.

Vancouver:

Ziegler C. On Factors of Rank One Subshifts. [Internet] [Thesis]. University of North Texas; 2018. [cited 2020 Feb 22]. Available from: https://digital.library.unt.edu/ark:/67531/metadc1157623/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ziegler C. On Factors of Rank One Subshifts. [Thesis]. University of North Texas; 2018. Available from: https://digital.library.unt.edu/ark:/67531/metadc1157623/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Guelph

7. Etbaigha, Fatima. Nonunique Equilibria of Projected Dynamical Systems and Their Applications .

Degree: 2018, University of Guelph

URL: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/14192

► Projected dynamical systems were formulated in the 1990s by Dupuis and Nagurney. In contrast to classical dynamical systems, projected dynamical systems have discontinuous right hand… (more)

▼ Projected dynamical systems were formulated in the 1990s by Dupuis and Nagurney. In contrast to classical dynamical systems, projected dynamical systems have discontinuous right hand sides that are associated with a projection operator. By the projection mecha- nism, the whole Hilbert space H is projected onto a non-empty, closed convex set K ⊂ H. Critical points of a projected dynamical system coincide with the solutions of a corresponding variational inequality problem; therefore, the applications of projected dynamical systems have been found in various fields such as economics, operations research and engineering. In this thesis, we study applications of equilibria of projected dynamical systems for market equilibrium problems, games and compartmental population models. First, the well-known market disequilibrium model with excess supply and demand is investigated to determine if it exhibits changes in the structure and the number of equilibrium states for specific choices of parameter values. We study the bifurcation problem (i.e., a qualitative change in equilib- rium states) as a parameterized variational inequality problem. We conduct our analysis by modeling the markets via a projected dynamical system. Second, we present a combination of theoretical and computational results meant to give insights into the question of the existence of nonunique Nash equilibria for N-player nonlinear games. Our inquiries make use of the theory of variational inequalities and projected systems to classify cases where multiplayer Nash games with parameterized payoffs exhibit changes in the number of Nash equilibria, depending on given parameter values. Finally, we use the compartmental popu- lation model, namely, the deterministic Susceptible-Exposed-Infectious-Recovered model, to analyze the dynamics of influenza infection of a farrow-to-finish swine farm, and we explore the reinfection at the farm level. We further examine the effectiveness of two control strate- gies: vaccination and reduction of indirect contact. In this case, we show that the model is a projected dynamical system but the projection does not add any relevant applied meaning to the results. Therefore, we show that the problem can be studied using classical dynamical systems. Advisors/Committee Members: Cojocaru, Fatima (advisor).

Subjects/Keywords: Projected dynamical systems

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APA (6^th Edition):

Etbaigha, F. (2018). Nonunique Equilibria of Projected Dynamical Systems and Their Applications . (Thesis). University of Guelph. Retrieved from https://atrium.lib.uoguelph.ca/xmlui/handle/10214/14192

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Etbaigha, Fatima. “Nonunique Equilibria of Projected Dynamical Systems and Their Applications .” 2018. Thesis, University of Guelph. Accessed February 22, 2020. https://atrium.lib.uoguelph.ca/xmlui/handle/10214/14192.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Etbaigha, Fatima. “Nonunique Equilibria of Projected Dynamical Systems and Their Applications .” 2018. Web. 22 Feb 2020.

Vancouver:

Etbaigha F. Nonunique Equilibria of Projected Dynamical Systems and Their Applications . [Internet] [Thesis]. University of Guelph; 2018. [cited 2020 Feb 22]. Available from: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/14192.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Etbaigha F. Nonunique Equilibria of Projected Dynamical Systems and Their Applications . [Thesis]. University of Guelph; 2018. Available from: https://atrium.lib.uoguelph.ca/xmlui/handle/10214/14192

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Purdue University

8. Alvey, Christina M. Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases.

Degree: PhD, Mathematics, 2015, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/414

► This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of… (more)

▼ This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of the three coupled disease models addresses different epidemiological questions with regard to gender or disease structure in the context of sexually-transmitted diseases (STDs), while the malaria model focuses on age-structure of the human population. ^ Mounting evidence indicates that HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the epidemiological synergy between HIV and HSV-2, we formulate, in Chapter 2, a deterministic compartmental model that describes the transmission dynamics of these diseases. Unlike earlier models, ours incorporates gender and heterogeneous mixing between activity groups. We derive explicit expressions for the basic and invasion reproduction numbers of HSV-2 and HIV. A qualitative analysis of the system includes the local and global behavior of the model. Simulations reinforce these analytical results and demonstrate epidemiological synergy between HSV-2 and HIV. Most importantly, we illustrate that the disease dynamics can be significantly influenced by the sexual structure of the population. ^ Chapter 3 deals with another model for HIV and HSV-2 using a different approach, which allows us to better capture the unique epidemiological feature of HSV-2 and its effect on the disease dynamics of HIV. As HSV-2 is an incurable viral infection, characterized by periodic reactivation, we construct a model of the co-infection dynamics by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. We also incorporate gender and activity groups in this model. The basic and invasion reproduction numbers are derived and interpreted. The calculations of the invasion reproduction numbers suggest a new interpretation: the class from which the initial disease carrier arises is important for understanding the invasion dynamics. Numerical simulations and a sensitivity analysis are conducted. Results illustrate the importance of including risk groups in the model. Treatment implications are discussed. ^ As the previous studies of HIV and HSV-2 focus only on a heterosexual population, Chapter 4 introduces a model with both heterosexual and homosexual interactions. We derive and interpret the basic and invasion reproduction numbers for HIV and HSV-2 using the approach of next-generation matrices. We then perform scenario analyses and conduct a sensitivity analysis to investigate the impact of model parameters on the reproduction numbers and disease prevalences. We conclude that homosexual transmission drastically changes the disease prevalences and that models that ignore homosexuality may greatly underestimate the disease burden; hence, it is important to account for this… Advisors/Committee Members: Zhilan Feng, Zhilan Feng, John W Glasser, Greg Buzzard, NK Yip.

Subjects/Keywords: Dynamical Systems; Mathematics

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APA (6^th Edition):

Alvey, C. M. (2015). Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/414

Chicago Manual of Style (16^th Edition):

Alvey, Christina M. “Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases.” 2015. Doctoral Dissertation, Purdue University. Accessed February 22, 2020. https://docs.lib.purdue.edu/open_access_dissertations/414.

MLA Handbook (7^th Edition):

Alvey, Christina M. “Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases.” 2015. Web. 22 Feb 2020.

Vancouver:

Alvey CM. Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases. [Internet] [Doctoral dissertation]. Purdue University; 2015. [cited 2020 Feb 22]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/414.

Council of Science Editors:

Alvey CM. Investigating synergy: Mathematical models for the coupled dynamics of HIV and HSV-2 and other endemic diseases. [Doctoral Dissertation]. Purdue University; 2015. Available from: https://docs.lib.purdue.edu/open_access_dissertations/414

Georgia Tech

9. Bolding, Mark M. Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.

Degree: PhD, Mathematics, 2018, Georgia Tech

URL: http://hdl.handle.net/1853/59931

► We prove that the evolution of the "most chaotic" dynamical systems consists of three different stages. Consider a finite Markov partition (coarse graining) X of… (more)

Subjects/Keywords: Dynamical systems; Chaos

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APA (6^th Edition):

Bolding, M. M. (2018). Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59931

Chicago Manual of Style (16^th Edition):

Bolding, Mark M. “Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.” 2018. Doctoral Dissertation, Georgia Tech. Accessed February 22, 2020. http://hdl.handle.net/1853/59931.

MLA Handbook (7^th Edition):

Bolding, Mark M. “Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model.” 2018. Web. 22 Feb 2020.

Vancouver:

Bolding MM. Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. [Internet] [Doctoral dissertation]. Georgia Tech; 2018. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1853/59931.

Council of Science Editors:

Bolding MM. Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model. [Doctoral Dissertation]. Georgia Tech; 2018. Available from: http://hdl.handle.net/1853/59931

University of Oklahoma

10. LaBryer, Allen Russell. Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems.

Degree: PhD, 2012, University of Oklahoma

URL: http://hdl.handle.net/11244/318987

► We investigate the performance of the subgrid-scale models with under-resolved simulations (in space and time) and various discretization schemes. For the canonical Duffing and van… (more)

Subjects/Keywords: Nonlinear systems; Differentiable dynamical systems

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APA (6^th Edition):

LaBryer, A. R. (2012). Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/318987

Chicago Manual of Style (16^th Edition):

LaBryer, Allen Russell. “Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems.” 2012. Doctoral Dissertation, University of Oklahoma. Accessed February 22, 2020. http://hdl.handle.net/11244/318987.

MLA Handbook (7^th Edition):

LaBryer, Allen Russell. “Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems.” 2012. Web. 22 Feb 2020.

Vancouver:

LaBryer AR. Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems. [Internet] [Doctoral dissertation]. University of Oklahoma; 2012. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/11244/318987.

Council of Science Editors:

LaBryer AR. Optimal Spatiotemporal Reduced Order Modeling for Nonlinear Dynamical Systems. [Doctoral Dissertation]. University of Oklahoma; 2012. Available from: http://hdl.handle.net/11244/318987

Dalhousie University

11. Alhulaimi, Bassemah. ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS.

Degree: MS, Department of Mathematics & Statistics - Math Division, 2012, Dalhousie University

URL: http://hdl.handle.net/10222/15391

► This thesis consists of two parts. In the first part, which is expository, abstract theory of one-parameter operator is studied semi-groups. We develop in detail… (more)

Subjects/Keywords: SEMIGROUPS AND DYNAMICAL SYSTEMS

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APA (6^th Edition):

Alhulaimi, B. (2012). ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS. (Masters Thesis). Dalhousie University. Retrieved from http://hdl.handle.net/10222/15391

Chicago Manual of Style (16^th Edition):

Alhulaimi, Bassemah. “ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS.” 2012. Masters Thesis, Dalhousie University. Accessed February 22, 2020. http://hdl.handle.net/10222/15391.

MLA Handbook (7^th Edition):

Alhulaimi, Bassemah. “ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS.” 2012. Web. 22 Feb 2020.

Vancouver:

Alhulaimi B. ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS. [Internet] [Masters thesis]. Dalhousie University; 2012. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/10222/15391.

Council of Science Editors:

Alhulaimi B. ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS. [Masters Thesis]. Dalhousie University; 2012. Available from: http://hdl.handle.net/10222/15391

University of Pretoria

12. Beyers, Frederik Johannes Conradie. The Szemerédi property in noncommutative dynamical systems.

Degree: Mathematics and Applied Mathematics, 2009, University of Pretoria

URL: http://hdl.handle.net/2263/24940

Subjects/Keywords: Noncommutative dynamical systems; UCTD

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APA (6^th Edition):

Beyers, F. J. (2009). The Szemerédi property in noncommutative dynamical systems. (Doctoral Dissertation). University of Pretoria. Retrieved from http://hdl.handle.net/2263/24940

Chicago Manual of Style (16^th Edition):

Beyers, Frederik Johannes. “The Szemerédi property in noncommutative dynamical systems.” 2009. Doctoral Dissertation, University of Pretoria. Accessed February 22, 2020. http://hdl.handle.net/2263/24940.

MLA Handbook (7^th Edition):

Beyers, Frederik Johannes. “The Szemerédi property in noncommutative dynamical systems.” 2009. Web. 22 Feb 2020.

Vancouver:

Beyers FJ. The Szemerédi property in noncommutative dynamical systems. [Internet] [Doctoral dissertation]. University of Pretoria; 2009. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/2263/24940.

Council of Science Editors:

Beyers FJ. The Szemerédi property in noncommutative dynamical systems. [Doctoral Dissertation]. University of Pretoria; 2009. Available from: http://hdl.handle.net/2263/24940

University of New Mexico

13. Siddique, Abu Bakar. Symmetries in the time-averaged dynamics of stochastic models of networks dynamics.

Degree: Mechanical Engineering, 2016, University of New Mexico

URL: http://hdl.handle.net/1928/32987

► In recent years a large body of research has investigated the dynamics of complex networks, including percolation [1, 2], epidemics [3, 4], synchronization [5, 6],… (more)

Subjects/Keywords: symmetry; dynamical systems; complex network

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APA (6^th Edition):

Siddique, A. B. (2016). Symmetries in the time-averaged dynamics of stochastic models of networks dynamics. (Masters Thesis). University of New Mexico. Retrieved from http://hdl.handle.net/1928/32987

Chicago Manual of Style (16^th Edition):

Siddique, Abu Bakar. “Symmetries in the time-averaged dynamics of stochastic models of networks dynamics.” 2016. Masters Thesis, University of New Mexico. Accessed February 22, 2020. http://hdl.handle.net/1928/32987.

MLA Handbook (7^th Edition):

Siddique, Abu Bakar. “Symmetries in the time-averaged dynamics of stochastic models of networks dynamics.” 2016. Web. 22 Feb 2020.

Vancouver:

Siddique AB. Symmetries in the time-averaged dynamics of stochastic models of networks dynamics. [Internet] [Masters thesis]. University of New Mexico; 2016. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1928/32987.

Council of Science Editors:

Siddique AB. Symmetries in the time-averaged dynamics of stochastic models of networks dynamics. [Masters Thesis]. University of New Mexico; 2016. Available from: http://hdl.handle.net/1928/32987

14. Yohannes, Arega W. Dynamic Programming.

Degree: MS, Mathematical Sciences, 1981, Clark University Atlanta

URL: http://digitalcommons.auctr.edu/dissertations/351

► The fundamental goal, in preparing this thesis, is two-fold. First, the author shows the systematic development of the basic theory of Dynamic Programming. Secondly,… (more)

Subjects/Keywords: Dynamical Systems

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APA (6^th Edition):

Yohannes, A. W. (1981). Dynamic Programming. (Thesis). Clark University Atlanta. Retrieved from http://digitalcommons.auctr.edu/dissertations/351

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yohannes, Arega W. “Dynamic Programming.” 1981. Thesis, Clark University Atlanta. Accessed February 22, 2020. http://digitalcommons.auctr.edu/dissertations/351.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yohannes, Arega W. “Dynamic Programming.” 1981. Web. 22 Feb 2020.

Vancouver:

Yohannes AW. Dynamic Programming. [Internet] [Thesis]. Clark University Atlanta; 1981. [cited 2020 Feb 22]. Available from: http://digitalcommons.auctr.edu/dissertations/351.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yohannes AW. Dynamic Programming. [Thesis]. Clark University Atlanta; 1981. Available from: http://digitalcommons.auctr.edu/dissertations/351

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Oregon State University

15. Schmurr, Jason Peter. Triangular billiards surfaces and translation covers.

Degree: PhD, Mathematics, 2008, Oregon State University

URL: http://hdl.handle.net/1957/9950

► We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards… (more)

Subjects/Keywords: Billiards; Differentiable dynamical systems

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APA (6^th Edition):

Schmurr, J. P. (2008). Triangular billiards surfaces and translation covers. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/9950

Chicago Manual of Style (16^th Edition):

Schmurr, Jason Peter. “Triangular billiards surfaces and translation covers.” 2008. Doctoral Dissertation, Oregon State University. Accessed February 22, 2020. http://hdl.handle.net/1957/9950.

MLA Handbook (7^th Edition):

Schmurr, Jason Peter. “Triangular billiards surfaces and translation covers.” 2008. Web. 22 Feb 2020.

Vancouver:

Schmurr JP. Triangular billiards surfaces and translation covers. [Internet] [Doctoral dissertation]. Oregon State University; 2008. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1957/9950.

Council of Science Editors:

Schmurr JP. Triangular billiards surfaces and translation covers. [Doctoral Dissertation]. Oregon State University; 2008. Available from: http://hdl.handle.net/1957/9950

University of Pretoria

16. [No author]. The Szemerédi property in noncommutative dynamical systems .

Degree: 2009, University of Pretoria

URL: http://upetd.up.ac.za/thesis/available/etd-05242009-145506/

Subjects/Keywords: Noncommutative dynamical systems; UCTD

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APA (6^th Edition):

author], [. (2009). The Szemerédi property in noncommutative dynamical systems . (Doctoral Dissertation). University of Pretoria. Retrieved from http://upetd.up.ac.za/thesis/available/etd-05242009-145506/

Chicago Manual of Style (16^th Edition):

author], [No. “The Szemerédi property in noncommutative dynamical systems .” 2009. Doctoral Dissertation, University of Pretoria. Accessed February 22, 2020. http://upetd.up.ac.za/thesis/available/etd-05242009-145506/.

MLA Handbook (7^th Edition):

author], [No. “The Szemerédi property in noncommutative dynamical systems .” 2009. Web. 22 Feb 2020.

Vancouver:

author] [. The Szemerédi property in noncommutative dynamical systems . [Internet] [Doctoral dissertation]. University of Pretoria; 2009. [cited 2020 Feb 22]. Available from: http://upetd.up.ac.za/thesis/available/etd-05242009-145506/.

Council of Science Editors:

author] [. The Szemerédi property in noncommutative dynamical systems . [Doctoral Dissertation]. University of Pretoria; 2009. Available from: http://upetd.up.ac.za/thesis/available/etd-05242009-145506/

University of Western Australia

17. Whiteside, David. The effect of constraints on the elite female tennis serve : a developmental perspective.

Degree: PhD, 2012, University of Western Australia

URL: http://repository.uwa.edu.au:80/R/?func=dbin-jump-full&object_id=34897&local_base=GEN01-INS01

►

[Truncated abstract] The serve has been described as the most important stroke in tennis, as it provides a player with an opportunity to gain the… (more)

▼

[Truncated abstract] The serve has been described as the most important stroke in tennis, as it provides a player with an opportunity to gain the ascendency in a point, or even win it outright. It is used to start each point and, as a closed motor skill, is the only stroke that affords the player complete control over its execution. The importance of the stroke is apparent given the amount of research attention it has generated. Contemporary practical instruction has been developed from this research base, however the disproportionate research focus on adult males limits the applicability of empirical findings to other playing populations. Consequently, the evolution of service kinematics along the development pathway (i.e. from junior through to professional levels) is poorly understood. With considerable monetary investments afforded to the pathway, exploring serve development appears relevant to high performance coaches and administrators. At present, the available literature has described the discrete kinematics crucial to the generation of velocity in the tennis serve. These data provide reference points for coaches, who attend to these mechanics in their evaluation of serve performance. However, with these data largely borne out of research attending to adult males, coaches of female and junior players must effectively rely on extraneous evidence, or extrapolate information, as they develop their instructional techniques. The motor literature challenges this approach and advocates an appreciation for gender and age related differences in service kinematics. Specifically, Newell's constraints model (1986) proposes that, within the dynamic movement system, emergent movement patterns are a product of the interactive elements within the organism, task and environment. Within this constraints framework, there appears sufficient scope to extend the current understanding of serve mechanics.

This thesis is presented as a series of papers, each extending the understanding of serve performance in previously neglected populations. The first study aimed to establish how organismic constraints affect the kinematics critical to the performance of the elite female serve. Three-dimensional body kinematics of pre-pubescent (11-12 years), pubescent (14- 15 years) and adult (18+ years) players were recorded as they performed five successful maximal effort flat serves aiming at a 1 × 1 m target bordering the T of the service box. The variables considered critical to serve performance in males formed the basis of the analysis of the high-performance junior and elite professional female cohorts. The results indicated that the role of the serving arm appears to become more pronounced after the onset of puberty, while leg drive and 'shoulder-over-shoulder' rotation mature even later in development. Furthermore, coupling perceptual cues from the ball toss with preparatory movements appeared less refined in pre-pubescent players. Ultimately, progression along the development pathway appears to transform the manner in which players…

Subjects/Keywords: Tennis; Development; Dynamical systems; Biomechanics

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APA (6^th Edition):

Whiteside, D. (2012). The effect of constraints on the elite female tennis serve : a developmental perspective. (Doctoral Dissertation). University of Western Australia. Retrieved from http://repository.uwa.edu.au:80/R/?func=dbin-jump-full&object_id=34897&local_base=GEN01-INS01

Chicago Manual of Style (16^th Edition):

Whiteside, David. “The effect of constraints on the elite female tennis serve : a developmental perspective.” 2012. Doctoral Dissertation, University of Western Australia. Accessed February 22, 2020. http://repository.uwa.edu.au:80/R/?func=dbin-jump-full&object_id=34897&local_base=GEN01-INS01.

MLA Handbook (7^th Edition):

Whiteside, David. “The effect of constraints on the elite female tennis serve : a developmental perspective.” 2012. Web. 22 Feb 2020.

Vancouver:

Whiteside D. The effect of constraints on the elite female tennis serve : a developmental perspective. [Internet] [Doctoral dissertation]. University of Western Australia; 2012. [cited 2020 Feb 22]. Available from: http://repository.uwa.edu.au:80/R/?func=dbin-jump-full&object_id=34897&local_base=GEN01-INS01.

Council of Science Editors:

Whiteside D. The effect of constraints on the elite female tennis serve : a developmental perspective. [Doctoral Dissertation]. University of Western Australia; 2012. Available from: http://repository.uwa.edu.au:80/R/?func=dbin-jump-full&object_id=34897&local_base=GEN01-INS01

Penn State University

18. Ho, Wing Kai. On Geodesics of Compact Riemannian Surfaces.

Degree: PhD, Mathematics, 2009, Penn State University

URL: https://etda.libraries.psu.edu/catalog/10159

► This dissertation is divided into two parts. In part one we deal with the 1/k length spectrum of a compact Riemannian manifold. The 1/k spectrum… (more)

Subjects/Keywords: dynamical systems; Riemannian geometry; geodesics

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APA (6^th Edition):

Ho, W. K. (2009). On Geodesics of Compact Riemannian Surfaces. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10159

Chicago Manual of Style (16^th Edition):

Ho, Wing Kai. “On Geodesics of Compact Riemannian Surfaces.” 2009. Doctoral Dissertation, Penn State University. Accessed February 22, 2020. https://etda.libraries.psu.edu/catalog/10159.

MLA Handbook (7^th Edition):

Ho, Wing Kai. “On Geodesics of Compact Riemannian Surfaces.” 2009. Web. 22 Feb 2020.

Vancouver:

Ho WK. On Geodesics of Compact Riemannian Surfaces. [Internet] [Doctoral dissertation]. Penn State University; 2009. [cited 2020 Feb 22]. Available from: https://etda.libraries.psu.edu/catalog/10159.

Council of Science Editors:

Ho WK. On Geodesics of Compact Riemannian Surfaces. [Doctoral Dissertation]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/10159

University of Victoria

19. Foxall, Eric. A contraction argument for two-dimensional spiking neuron models.

Degree: Dept. of Mathematics and Statistics, 2011, University of Victoria

URL: http://hdl.handle.net/1828/3459

► The field of mathematical neuroscience is concerned with the modeling and interpretation of neuronal dynamics and associated phenomena. Neurons can be modeled individually, in small… (more)

Subjects/Keywords: Dynamical Systems; Mathematical Neuroscience

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APA (6^th Edition):

Foxall, E. (2011). A contraction argument for two-dimensional spiking neuron models. (Masters Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/3459

Chicago Manual of Style (16^th Edition):

Foxall, Eric. “A contraction argument for two-dimensional spiking neuron models.” 2011. Masters Thesis, University of Victoria. Accessed February 22, 2020. http://hdl.handle.net/1828/3459.

MLA Handbook (7^th Edition):

Foxall, Eric. “A contraction argument for two-dimensional spiking neuron models.” 2011. Web. 22 Feb 2020.

Vancouver:

Foxall E. A contraction argument for two-dimensional spiking neuron models. [Internet] [Masters thesis]. University of Victoria; 2011. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1828/3459.

Council of Science Editors:

Foxall E. A contraction argument for two-dimensional spiking neuron models. [Masters Thesis]. University of Victoria; 2011. Available from: http://hdl.handle.net/1828/3459

Boston University

20. Cuzzocreo, Daniel L. Dynamical invariants and parameter space structures for rational maps.

Degree: PhD, Mathematics & Statistics, 2014, Boston University

URL: http://hdl.handle.net/2144/15115

► For parametrized families of dynamical systems, two major goals are classifying the systems up to topological conjugacy, and understanding the structure of the bifurcation locus.… (more)

Subjects/Keywords: Mathematics; Complex dynamics; Dynamical systems

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APA (6^th Edition):

Cuzzocreo, D. L. (2014). Dynamical invariants and parameter space structures for rational maps. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/15115

Chicago Manual of Style (16^th Edition):

Cuzzocreo, Daniel L. “Dynamical invariants and parameter space structures for rational maps.” 2014. Doctoral Dissertation, Boston University. Accessed February 22, 2020. http://hdl.handle.net/2144/15115.

MLA Handbook (7^th Edition):

Cuzzocreo, Daniel L. “Dynamical invariants and parameter space structures for rational maps.” 2014. Web. 22 Feb 2020.

Vancouver:

Cuzzocreo DL. Dynamical invariants and parameter space structures for rational maps. [Internet] [Doctoral dissertation]. Boston University; 2014. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/2144/15115.

Council of Science Editors:

Cuzzocreo DL. Dynamical invariants and parameter space structures for rational maps. [Doctoral Dissertation]. Boston University; 2014. Available from: http://hdl.handle.net/2144/15115

Cornell University

21. Wesson, Elizabeth. Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing .

Degree: 2015, Cornell University

URL: http://hdl.handle.net/1813/40628

► Evolutionary dynamics combines game theory and nonlinear dynamics to model competition in biological and social situations. The replicator equation is a standard paradigm in evolutionary… (more)

Subjects/Keywords: evolutionary dynamics; dynamical systems; perturbation

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APA (6^th Edition):

Wesson, E. (2015). Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/40628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wesson, Elizabeth. “Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing .” 2015. Thesis, Cornell University. Accessed February 22, 2020. http://hdl.handle.net/1813/40628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wesson, Elizabeth. “Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing .” 2015. Web. 22 Feb 2020.

Vancouver:

Wesson E. Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing . [Internet] [Thesis]. Cornell University; 2015. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1813/40628.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wesson E. Replicator Dynamics With Alternate Growth Functions, Delay, And Quasiperiodic Forcing . [Thesis]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/40628

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oklahoma

22. Bauer, Sean. ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.

Degree: PhD, 2016, University of Oklahoma

URL: http://hdl.handle.net/11244/34745

► We prove the existence of a torus that is invariant with respect to the flow of a presymplectic vector field found in a family of… (more)

Subjects/Keywords: Dynamical Systems; Presymplectic; KAM

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APA (6^th Edition):

Bauer, S. (2016). ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/34745

Chicago Manual of Style (16^th Edition):

Bauer, Sean. “ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.” 2016. Doctoral Dissertation, University of Oklahoma. Accessed February 22, 2020. http://hdl.handle.net/11244/34745.

MLA Handbook (7^th Edition):

Bauer, Sean. “ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS.” 2016. Web. 22 Feb 2020.

Vancouver:

Bauer S. ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2016. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/11244/34745.

Council of Science Editors:

Bauer S. ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS. [Doctoral Dissertation]. University of Oklahoma; 2016. Available from: http://hdl.handle.net/11244/34745

University of New South Wales

23. Stuart, Robyn. Metastable sets in open dynamical systems and substochastic Markov chains.

Degree: Mathematics & Statistics, 2014, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/53827 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12540/SOURCE02?view=true

► In this thesis we look at dynamical systems in which typical trajectories (1) have a non-zero probability of exiting the state space and (2) before… (more)

▼ In this thesis we look at dynamical systems in which typical trajectories (1) have a non-zero probability of exiting the state space and (2) before exiting, tend to remain in one proper subset of the state space for a long time. The first property defines an open dynamical system and the second property is called metastability. Sets in which trajectories remain for a long time are called metastable or almost-invariant sets. The major contribution of this thesis is the development of techniques to locate and characterise metastable sets in open dynamical systems.In closed dynamical systems, there are well-established connections between the spectrum of the Perron-Frobenius operator and the metastability properties of the system. After introducing the research aims in Chapter 1, we review the existing literature and establish notation in Chapter 2. One can use the eigenfunctions of the transfer operator to locate metastable sets, and one can derive bounds on the maximal invariance ratio of a set in terms of the second largest eigenvalue of a discretised version of the Perron-Frobenius operator. In Chapters 3 and 4 we extend these techniques to open dynamical systems. Chapter 3 introduces a new closing operation for open systems that has a minimal effect on the metastability properties, and allows us to apply existing techniques for closed systems to locate metastable sets, and to derive bounds on the maximal invariance ratio in terms of the second largest eigenvalue of the new operator. In Chapter 4 we derive bounds on the metastability and the conductance of substochastic Markov chains, which can be related to discretised transfer operators for open dynamical systems. Both conductance and metastability quantify how well subsets of states interact and mix. In Chapter 5 we apply some of the techniques developed in previous chapters to a global ocean model, and characterise the connectivity of the surface of the ocean using both absorption probabilities and eigenvector methods. Advisors/Committee Members: Froyland, Gary, Mathematics & Statistics, Faculty of Science, UNSW.

Subjects/Keywords: Metastable sets; Dynamical systems

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APA (6^th Edition):

Stuart, R. (2014). Metastable sets in open dynamical systems and substochastic Markov chains. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/53827 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12540/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Stuart, Robyn. “Metastable sets in open dynamical systems and substochastic Markov chains.” 2014. Doctoral Dissertation, University of New South Wales. Accessed February 22, 2020. http://handle.unsw.edu.au/1959.4/53827 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12540/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Stuart, Robyn. “Metastable sets in open dynamical systems and substochastic Markov chains.” 2014. Web. 22 Feb 2020.

Vancouver:

Stuart R. Metastable sets in open dynamical systems and substochastic Markov chains. [Internet] [Doctoral dissertation]. University of New South Wales; 2014. [cited 2020 Feb 22]. Available from: http://handle.unsw.edu.au/1959.4/53827 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12540/SOURCE02?view=true.

Council of Science Editors:

Stuart R. Metastable sets in open dynamical systems and substochastic Markov chains. [Doctoral Dissertation]. University of New South Wales; 2014. Available from: http://handle.unsw.edu.au/1959.4/53827 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:12540/SOURCE02?view=true

University of New South Wales

24. Truant, Daniel. The covariant Lyapunov analysis of chaotic dynamical systems.

Degree: Physics, 2013, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/52460 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11133/SOURCE01?view=true

► In this thesis the Lyapunov analysis, as applied to the chaotic dynamics of quasi one dimensional hark disk systems, is extended to the covariant Lyapunov… (more)

▼ In this thesis the Lyapunov analysis, as applied to the chaotic dynamics of quasi one dimensional hark disk systems, is extended to the covariant Lyapunov vectors of both equilibrium and deterministic nonequilibrium steady states. Previously, the Lyapunov analysis of chaotic dynamics has solely utilised the backward Lyapunov vectors (BLVs) as calculated via the Benettin scheme. In recent years Ginelli et al. found an effective and realistically employable algorithm to calculate the covariant Lyapunov vectors (CLVs). In this thesis the CLVs are analysed, the evolution of the covariant hydrodynamic Lyapunov modes are derived exactly via the reverse tangent space dynamics and their properties are compared with the well-known BLVs. The converged angle between the hydrodynamic stable and unstable conjugate manifolds of the tangent space are predicted to high accuracy. Intriguing aspects and new interpretations are also presented of the evolution and characteristics of the BLVs, derived directly from the forward tangent space dynamics. The covariant Lyapunov analysis is generalised to systems attached to deterministic thermal reservoirs. The thermal reservoirs create a heat current across the system and perturb it away from equilibrium. In this thesis the augmentation of the Lyapunov exponents as a function of heat current is described and explained. Both the nonequilibrium backward and covariant hydrodynamic Lyapunov modes are analysed and compared for the first time. With the free flight time of the dynamics, the movement of the converged angle between the hydrodynamic stable and unstable conjugate manifolds is accurately predicted for any nonequilibrium system simply as a function of their exponent. The nonequilibrium positive and negative LP mode frequencies are found to be asymmetrical, causing the negative mode to oscillate between taking the functional forms of each mode in the positive conjugate mode pair. This in turn leads to the angular distributions between the conjugate modes to oscillate symmetrically about pi/2 at a rate given by the difference between the positive and negative mode frequencies. Advisors/Committee Members: Morriss, Gary, Physics, Faculty of Science, UNSW.

Subjects/Keywords: Dynamical systems; Covariant; Lyapunov

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APA (6^th Edition):

Truant, D. (2013). The covariant Lyapunov analysis of chaotic dynamical systems. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/52460 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11133/SOURCE01?view=true

Chicago Manual of Style (16^th Edition):

Truant, Daniel. “The covariant Lyapunov analysis of chaotic dynamical systems.” 2013. Doctoral Dissertation, University of New South Wales. Accessed February 22, 2020. http://handle.unsw.edu.au/1959.4/52460 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11133/SOURCE01?view=true.

MLA Handbook (7^th Edition):

Truant, Daniel. “The covariant Lyapunov analysis of chaotic dynamical systems.” 2013. Web. 22 Feb 2020.

Vancouver:

Truant D. The covariant Lyapunov analysis of chaotic dynamical systems. [Internet] [Doctoral dissertation]. University of New South Wales; 2013. [cited 2020 Feb 22]. Available from: http://handle.unsw.edu.au/1959.4/52460 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11133/SOURCE01?view=true.

Council of Science Editors:

Truant D. The covariant Lyapunov analysis of chaotic dynamical systems. [Doctoral Dissertation]. University of New South Wales; 2013. Available from: http://handle.unsw.edu.au/1959.4/52460 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11133/SOURCE01?view=true

University of Waterloo

25. Horrocks, Jonathan H. Sparse Identification of Epidemiological Models from Empirical Data.

Degree: 2018, University of Waterloo

URL: http://hdl.handle.net/10012/13864

► Current modelling practices in mathematical epidemiology are predicated on mechanisms stemming from theoretical assumptions, such as mass action incidence. Deterministic disease models can describe many… (more)

▼ Current modelling practices in mathematical epidemiology are predicated on mechanisms stemming from theoretical assumptions, such as mass action incidence. Deterministic disease models can describe many patterns observed in empirical incidence data but challenges remain in creating accurate, parsimonious models that other predictive value. Recent advances in data-driven techniques give rise to new model discovery methods that forego theoretical assumptions and attempt to create sparse, dynamic models directly from real-world data. Our goal is to apply these techniques to empirical case notification data of epidemiological systems, to either con rm current practices or give new insight not accessible by human intuition. We adapt a recently developed technique called Sparse Identification of Nonlinear Dynamics (SINDy), which has demonstrated ability to recover governing equations of complex dynamical systems. To lend insight into this process, the SINDy algorithm was first applied to simulated data from various forms of the SIR model, a standard compartmental model of epidemics. Several conversion processes were then utilized to recover both the susceptible and infectious classes from raw incidence data. Finally, the SINDy algorithm was applied to empirical data from measles, varicella, and rubella datasets, three diseases that other contrasting dynamic behaviour, and the resulting time-series and model coefficients were analysed. The resulting models closely mimic the dynamics of the empirical data, most notably the frequency of epidemics, for all three diseases considered. The coefficients discovered exhibit sparsity, though not to the extent that current compartmental models do. Similarities between the discovered model equations and fitted SIR models can be noted, including a strong dependence on the cross-term corresponding with the mass action incidence mechanism. These encouraging results indicate this data-driven technique may be of use in verifying and improving current theoretical models in mathematical epidemiology.

Subjects/Keywords: Epidemiology; Dynamical Systems; Statistical Modelling

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APA (6^th Edition):

Horrocks, J. H. (2018). Sparse Identification of Epidemiological Models from Empirical Data. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/13864

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Horrocks, Jonathan H. “Sparse Identification of Epidemiological Models from Empirical Data.” 2018. Thesis, University of Waterloo. Accessed February 22, 2020. http://hdl.handle.net/10012/13864.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Horrocks, Jonathan H. “Sparse Identification of Epidemiological Models from Empirical Data.” 2018. Web. 22 Feb 2020.

Vancouver:

Horrocks JH. Sparse Identification of Epidemiological Models from Empirical Data. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/10012/13864.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Horrocks JH. Sparse Identification of Epidemiological Models from Empirical Data. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/13864

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oklahoma

26. Lin, Chenxi. Problems in the design and operation of uncertain complex engineering systems.

Degree: PhD, 2011, University of Oklahoma

URL: http://hdl.handle.net/11244/318961

► In this dissertation, we consider two problems. The first one is a general approach to the optimal design of uncertain dynamical systems, where the uncertainty… (more)

Subjects/Keywords: Differentiable dynamical systems; Mathematical optimization

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APA (6^th Edition):

Lin, C. (2011). Problems in the design and operation of uncertain complex engineering systems. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/318961

Chicago Manual of Style (16^th Edition):

Lin, Chenxi. “Problems in the design and operation of uncertain complex engineering systems.” 2011. Doctoral Dissertation, University of Oklahoma. Accessed February 22, 2020. http://hdl.handle.net/11244/318961.

MLA Handbook (7^th Edition):

Lin, Chenxi. “Problems in the design and operation of uncertain complex engineering systems.” 2011. Web. 22 Feb 2020.

Vancouver:

Lin C. Problems in the design and operation of uncertain complex engineering systems. [Internet] [Doctoral dissertation]. University of Oklahoma; 2011. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/11244/318961.

Council of Science Editors:

Lin C. Problems in the design and operation of uncertain complex engineering systems. [Doctoral Dissertation]. University of Oklahoma; 2011. Available from: http://hdl.handle.net/11244/318961

University of New South Wales

27. Quinn, Mitchell S. The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems.

Degree: Chemistry, 2017, University of New South Wales

URL: http://handle.unsw.edu.au/1959.4/57237 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42935/SOURCE02?view=true

► H2CO is photolysed between 30000 cm-1 to 37500 cm-1 ascertaining the individual quantum yield of all fiveradical, molecular and triple fragmentation channels. Branching fractions are… (more)

▼ H2CO is photolysed between 30000 cm-1 to 37500 cm-1 ascertaining the individual quantum yield of all fiveradical, molecular and triple fragmentation channels. Branching fractions are extracted from H atom velocitymapped ion (VMI) images and speed correlated REMPI spectra of CO(v = 0, 1). The traditional transition state(TS) mechanism is dominant at the extremes of this energy range, with the radical channels on the T1 and Sosurfaces dominant elsewhere. The roaming channel branching fraction is constant, accounting for -20 % ofCO produced. Roaming occurs on a timescale shorter than the vibrational predissociation of HCO. Thequantum yield of the triple fragmentation channel grows exponentially above threshold and is well modelledby a modified double phase space theory (PST) model.The (2+1) REMPI spectrum of H2 via the E,F state was collected and assigned. Nuclear spin is conserved inboth the 'tight'-TS and roaming pathways. VMI images of H2 (v = 3 - 9, J = 0 -12) are collected following thephotodissociation of H2CO via the rR0(0), rR0(1), and rR1(1) transitions to the 2143 state. CO(v, J) distributionscorrelated with individual H2 (v, J) states reveal that the CO(v) rotational distributions from the 'tight'-transition state (TS) and roaming pathways are multimodal. The multimodal nature of these distributions iscaused by structure in the nuclear wave function mapping onto the product rotational distribution (i.e.rotation-reflection principle).Two roaming pathways are identified as the major pathways for the production of CO and CH4 from thephotodissociation of CH3CHO. The two components of the bimodal CO product state distribution areattributed to the H- and CH3-roaming channels. No clear signature of the 'tight'-TS channel is observed. H2 isdetected for the first time as a product of the unimolecular decay of CH3CHO in a jet. These products areassigned to the H-roaming mechanism, similar to that producing CO + CH4. This is the first example ofmultiple roaming channels on the same electronic state and of two roaming channels associated with asingle barrierless dissociation channel. The results demonstrate that roaming can be significant in chemicalreactions and outweigh traditional pathways. Advisors/Committee Members: Kable , Scott H. , Chemistry, Faculty of Science, UNSW.

Subjects/Keywords: Prototypical Dynamical Systems; Photodissociation; Aldehydes

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APA (6^th Edition):

Quinn, M. S. (2017). The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/57237 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42935/SOURCE02?view=true

Chicago Manual of Style (16^th Edition):

Quinn, Mitchell S. “The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems.” 2017. Doctoral Dissertation, University of New South Wales. Accessed February 22, 2020. http://handle.unsw.edu.au/1959.4/57237 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42935/SOURCE02?view=true.

MLA Handbook (7^th Edition):

Quinn, Mitchell S. “The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems.” 2017. Web. 22 Feb 2020.

Vancouver:

Quinn MS. The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems. [Internet] [Doctoral dissertation]. University of New South Wales; 2017. [cited 2020 Feb 22]. Available from: http://handle.unsw.edu.au/1959.4/57237 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42935/SOURCE02?view=true.

Council of Science Editors:

Quinn MS. The photodissociation of small Aldehydes: a refined understanding of prototypical dynamical systems. [Doctoral Dissertation]. University of New South Wales; 2017. Available from: http://handle.unsw.edu.au/1959.4/57237 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:42935/SOURCE02?view=true

University of Toronto

28. Yao, Yupeng. Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach.

Degree: 2012, University of Toronto

URL: http://hdl.handle.net/1807/33598

►

Output regulation problems are a class of problems that has high importance in systems control engineering. The solutions of such problems generally involve the design… (more)

Subjects/Keywords: Dynamical Systems; Output Regulation; 0544

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APA (6^th Edition):

Yao, Y. (2012). Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/33598

Chicago Manual of Style (16^th Edition):

Yao, Yupeng. “Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach.” 2012. Masters Thesis, University of Toronto. Accessed February 22, 2020. http://hdl.handle.net/1807/33598.

MLA Handbook (7^th Edition):

Yao, Yupeng. “Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach.” 2012. Web. 22 Feb 2020.

Vancouver:

Yao Y. Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach. [Internet] [Masters thesis]. University of Toronto; 2012. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/1807/33598.

Council of Science Editors:

Yao Y. Sufficient Conditions for Output Regulation on Metric and Banach Spaces - A Set-theoretic Approach. [Masters Thesis]. University of Toronto; 2012. Available from: http://hdl.handle.net/1807/33598

Rutgers University

29. Marcondes de Freitas, Michael. A class of input/output random systems: monotonicity and a small-gain theorem.

Degree: PhD, Mathematics, 2014, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/

►

We expand upon the theory of random dynamical systems (RDS) of L. Arnold, developing a theory of random dynamical systems with inputs and outputs (RDSIO)—an… (more)

Subjects/Keywords: Random dynamical systems; Monotonic functions

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APA (6^th Edition):

Marcondes de Freitas, M. (2014). A class of input/output random systems: monotonicity and a small-gain theorem. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/45341/

Chicago Manual of Style (16^th Edition):

Marcondes de Freitas, Michael. “A class of input/output random systems: monotonicity and a small-gain theorem.” 2014. Doctoral Dissertation, Rutgers University. Accessed February 22, 2020. https://rucore.libraries.rutgers.edu/rutgers-lib/45341/.

MLA Handbook (7^th Edition):

Marcondes de Freitas, Michael. “A class of input/output random systems: monotonicity and a small-gain theorem.” 2014. Web. 22 Feb 2020.

Vancouver:

Marcondes de Freitas M. A class of input/output random systems: monotonicity and a small-gain theorem. [Internet] [Doctoral dissertation]. Rutgers University; 2014. [cited 2020 Feb 22]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/.

Council of Science Editors:

Marcondes de Freitas M. A class of input/output random systems: monotonicity and a small-gain theorem. [Doctoral Dissertation]. Rutgers University; 2014. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/45341/

30. Mirzakhalili, Ehsan. Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity.

Degree: PhD, Mechanical Engineering, 2018, University of Michigan

URL: http://hdl.handle.net/2027.42/145921

► Neurodegenerative diseases such as Alzheimer’s disease (AD) are all results of neurons losing their normal functionality. However, the exact mechanics of neurodegeneration remains obscure. Most… (more)

▼ Neurodegenerative diseases such as Alzheimer’s disease (AD) are all results of neurons losing their normal functionality. However, the exact mechanics of neurodegeneration remains obscure. Most of the knowledge about this class of diseases is obtained by studying late stage patients. Therefore, the mechanism proceeding the late stages of such diseases are less understood. Better understanding of respective mechanisms can help developing in early diagnostic tools and techniques to enable more effective treatment methods. Analyzing the dynamics of neural systems can be the key to discover the underlying mechanisms, which lead to neurodegenerative diseases. The dynamics of neural systems can be studied in different scales. At subcellular level, dynamics of axonal transport plays an important role in AD. In particular, anterograde axonal transport conducted by kinesin-1, known conventionally as kinesin, is essential for maintaining functional synapses. The stochastic motion of kinesin in the presence of magnetic nanoparticles is studied. A novel reduced-order-model (ROM) is constructed to simulate the collective dynamics of magnetic nanoparticles that are delivered into cells. The ROM coupled with the kinesin model allows the quantification of the decrease in processivity of kinesin and in its average velocity under external loads caused by chains of magnetic nanoparticles. Changes in the properties of transport induced by perturbations have the potential to decipher normal transport from impaired transport in the state of disease. In single-cell level analysis, Ca2+ transients in ASH neuron of C. elegans model organism is studied in the context of biological conditions such as aging and oxidative stress. A novel mathematical model is established that can describe the unique Ca2+ transients of ASH neuron in C. elegans including its “on” and “off” response. The model provides insight into the mechanism that governs the observed Ca2+ dynamics in ASH neuron. Hence, the proposed mathematical model can be utilized as a tool that offers explanation for changes induced by aging or oxidative stress in the neuron based on the observed Ca2+ dynamics. Network level analysis of neurons does not require methods of extremely high spatial and temporal resolution compared to the analysis in subcellular and cellular level. Yet, malfunction in smaller scales can manifest themselves in dynamics of larger scales. In particular, impairment of synaptic connections and their dynamics can jeopardize the normal functionality of the brain in pathological conditions such as AD. The impact of synaptic deficiencies is investigated on robustness of persistence activity (essential for working memory, which is adversely affected by AD) in excitatory networks with different topologies. Networks with rich-clubs are shown to have higher robustness when their synapses are impaired. Hence, monitoring changes in the properties of the neural network can be utilized as a tool to detect defects in synaptic connections. Moreover, such defects are shown to be… Advisors/Committee Members: Epureanu, Bogdan (committee member), Booth, Victoria (committee member), Gourgou, Eleni (committee member), Liu, Allen Po-Chih (committee member), Zochowski, Michal R (committee member).

Subjects/Keywords: Dynamical Systems; Mechanical Engineering; Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mirzakhalili, E. (2018). Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/145921

Chicago Manual of Style (16^th Edition):

Mirzakhalili, Ehsan. “Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity.” 2018. Doctoral Dissertation, University of Michigan. Accessed February 22, 2020. http://hdl.handle.net/2027.42/145921.

MLA Handbook (7^th Edition):

Mirzakhalili, Ehsan. “Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity.” 2018. Web. 22 Feb 2020.

Vancouver:

Mirzakhalili E. Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity. [Internet] [Doctoral dissertation]. University of Michigan; 2018. [cited 2020 Feb 22]. Available from: http://hdl.handle.net/2027.42/145921.

Council of Science Editors:

Mirzakhalili E. Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity. [Doctoral Dissertation]. University of Michigan; 2018. Available from: http://hdl.handle.net/2027.42/145921

Open Access Theses and Dissertations