报告题目：Dynamics of a prey-predator model with generalist predators

主讲人：邹兰教授

时 间：2023年12月21日（周四）上午10：30

地 点：腾讯会议383-424-469

主办单位：理学院

主讲人简介：

邹兰，四川大学数学学院副教授。 2010年6月在四川大学获理学博士学位。曾两次访问美国迈阿密大学数学系。目前研究方向为微分方程与动力系统、生物数学，特别关注传染病传播动力学、病毒动力学、生态种群动力学等建模及其定性理论、分岔理论等。任中国数学会生物数学专委会委员，CSIAM数学生命科学专委会委员。研究结果发表在SIAM Appl Math, PLoS Neglect Trop Dis, Acta Tropic, J Theor Biol等国际期刊。先后主持国家自然科学基金青年基金、面上基金，参与国家自然科学基金重点基金一项。

摘要:

Consideration of generalist predators leads to relatively complex dynamics due to alternative food sources. Here we propose and analyze a prey-predator model with a generalist predator. The availability of alternative food sources for the predator and density-dependent growth rate induces not only bistability and tristability, but also more complicated dynamical behaviors. We study the possible number of positive equilibria and geometric configurations near them in detail. A systematic bifurcation analysis reveals the existence of the degenerate Bogdanov-Takens bifurcation of codimension four and degenerate Hopf bifurcation of codimension three. Degenerate local bifurcations with higher codimension are responsible for three limit cycles. Derivation of analytical conditions for three limit cycles for a suitable range of parameters is a crucial finding of this work.