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Rutgers University

1. Kennedy, Benjamin B. Differential delay equations with several fixed delays.

Degree: PhD, Mathematics, 2007, Rutgers University

We study nonlinear autonomous real-valued differential delay equations with several fixed delays x'(t) = sumi=1 D Fi(x(t-di)), where the Fi are continuous, have nonzero limits at plus and minus infinity, and are similar (in a sense we make precise) to step functions. Our focus is on periodic solutions, and our approach is to link the above problem to an appropriately related equation y'(t) = sumi=1 D hi(y(t-di)), where the hi are in fact step functions. Given a periodic solution of the second problem, we describe conditions under which this solution implies the existence of a similar periodic solution of the first problem. We also prove some results on stability of periodic solutions, and make a partial study of the global dynamics of the second problem.

Advisors/Committee Members: Kennedy, Benjamin B. (author), Nussbaum, Roger (chair), Sussmann, Hector (internal member), Sontag, Eduardo (internal member), Mallet-Paret, John (outside member).

Subjects/Keywords: Delay differential equations; Functional differential equations

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

APA (6th Edition):

Kennedy, B. B. (2007). Differential delay equations with several fixed delays. (Doctoral Dissertation). Rutgers University. Retrieved from http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409

Chicago Manual of Style (16th Edition):

Kennedy, Benjamin B. “Differential delay equations with several fixed delays.” 2007. Doctoral Dissertation, Rutgers University. Accessed January 18, 2021. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409.

MLA Handbook (7th Edition):

Kennedy, Benjamin B. “Differential delay equations with several fixed delays.” 2007. Web. 18 Jan 2021.

Vancouver:

Kennedy BB. Differential delay equations with several fixed delays. [Internet] [Doctoral dissertation]. Rutgers University; 2007. [cited 2021 Jan 18]. Available from: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409.

Council of Science Editors:

Kennedy BB. Differential delay equations with several fixed delays. [Doctoral Dissertation]. Rutgers University; 2007. Available from: http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16409

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