Reported by: Yancong XU (China Jiliang University)
Time: 15:30 October 22, 2024
Location: Room 401, Yifu Building
Abstract:
In this talk, we study a predator-prey mite model of Leslie typewith generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focus type and cusp-type degenerate Bogdanov-Takens bifurcations of codimension 3, originating fom a nilpotent focus or cusp of codimension 3 that acts as the organizing center for the bifurcation set. Coexistence of multiple steady states, multiple limit cycles, and homoclinic cycles is also found. Interestingly, the coexistence of two limmit cycles is guaranteed by investigating generalized Hopf bifurcation and degenerate homoclinic bifurcation, and we also find that two generalized Hopf bifurcation points are connected by a saddle-node bifurcation curve of limit cycles, which indicates the existence of global regime for two limit cycles and the nonexistence of isola of limit cycle. A Joint work with Yue Yang, Libin Rong and Shigui Ruan.
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