题目：Overexploitation occurs in the Rosenzweig-MacArthur model with trigonometric functional response
主讲人：徐衍聪， 杭州师范大学教授、博士生导师
时间：2020年11月10日，19:30-21:00
腾讯会议ID： 717 370 392，无密码
摘要：In this paper, we study a Rosenzweig-MacArthur predator-prey system with a strong Allee effect, and take a predator functional response to the hyperbolic tangent form as trigonometric. We study both the local and global dynamics, and the possible bifurcation is determined according to the variation of the carrying capacity of the prey. An analytic expression is given to determine the criticality of Hopf bifurcation, and the resulting Hopf bifurcation is proved to be supercritical or subcritical. The existence of heteroclinic orbit and Bautin bifurcation are also proved. Biologically speaking, such a heteroclinic cycle always forms a boundary of the region in two parameter space which indicates the breakdown of the system after the invasion of the predator, i.e., overexploitation occurs. Further, numerical simulations are given to demonstrate the theoretical results which include the coexistence of limit cycles and heteroclinic cycles.
主讲人简介：
徐衍聪：华东师范大学应用数学博士，浙江大学博士后，杭州师范大学数学系主任，教授，博士生导师，美国（SIAM）工业与应用数学会员，美国数学评论评论员。先后访问美国布朗大学、日本京都大学、德国不莱梅大学等高校。主要从事动力系统分支理论、局部斑图分支及应用研究，主要包括：Dynamical Systems, Dynamics of Patterns, Nonlinear Wave，Homoclinic and Heteroclinic Phenomena等研究工作。主持国家自然科学基金面上项目、浙江省自然科学基金， 日本GCOE项目及参与各类基金10余项。