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

2010, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Martin Golubitsky (Advisor)
Yuan Lou (Other)
James Cogdell (Other)
121 p.

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Zhang, Y. (2010). Periodic Forcing of a System near a Hopf Bifurcation Point. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Zhang, Yanyan. "Periodic Forcing of a System near a Hopf Bifurcation Point." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

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Zhang, Yanyan "Periodic Forcing of a System near a Hopf Bifurcation Point." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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