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Periodic Forcing of a System near a Hopf Bifurcation Point

Zhang, Yanyan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795

Abstract Details

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

Recommended Citations

Citations

  • Zhang, Y. (2010). Periodic Forcing of a System near a Hopf Bifurcation Point [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795

    APA Style (7th edition)

  • Zhang, Yanyan. Periodic Forcing of a System near a Hopf Bifurcation Point. 2010. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795.

    MLA Style (8th edition)

  • Zhang, Yanyan. "Periodic Forcing of a System near a Hopf Bifurcation Point." Doctoral dissertation, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291174795

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.