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The Ohio State University

1. Zhang, Yanyan. Periodic Forcing of a System near a Hopf Bifurcation Point.

Degree: PhD, Mathematics, 2010, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795

We study a periodically forced system of ODEs near a
point of Hopf bifurcation, where the forcing is pure harmonic with
small amplitude. We assume that the ratio of the Hopf frequency of
the ODE system and the forcing frequency is close to k/l where k
and l are coprime. We look for all small periodic solutions of the
forced system as the forcing frequency varies. In other words, we
examine the influence of the forcing frequency on the number of
periodic solutions to the forced system. This problem is
complicated because of the existence of three small parameters: the
amplitude of the forcing, the deviation of the bifurcation
parameter from the point of Hopf bifurcation, and the deviation of
the ratio of the Hopf and forcing frequencies from a rational
number. Our results are presented in terms of bifurcation diagrams
of amplitude of periodic solutions versus the forcing parameter for
fixed forcing amplitude and Hopf parameter.
*Advisors/Committee Members: Golubitsky, Martin (Advisor).*

Subjects/Keywords: Mathematics; Hopf bifurcation; Periodic forcing; S1 symmetry; Liapunov-Schmidt reduction; Normal Form; Universal unfolding; Singularity theory; Transition set

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APA (6^{th} Edition):

Zhang, Y. (2010). Periodic Forcing of a System near a Hopf Bifurcation Point. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795

Chicago Manual of Style (16^{th} Edition):

Zhang, Yanyan. “Periodic Forcing of a System near a Hopf Bifurcation Point.” 2010. Doctoral Dissertation, The Ohio State University. Accessed September 28, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795.

MLA Handbook (7^{th} Edition):

Zhang, Yanyan. “Periodic Forcing of a System near a Hopf Bifurcation Point.” 2010. Web. 28 Sep 2020.

Vancouver:

Zhang Y. Periodic Forcing of a System near a Hopf Bifurcation Point. [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2020 Sep 28]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795.

Council of Science Editors:

Zhang Y. Periodic Forcing of a System near a Hopf Bifurcation Point. [Doctoral Dissertation]. The Ohio State University; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795