题 目：Overexploitation occurs in the Rosenzweig-MacArthur model with trigonometric functional response
报告人：徐衍聪
时 间：2020年12月18日(星期五)，14:00-15:00
地 点：1-301
腾讯会议ID：602765744 会议密码：123456
报告摘要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.
报告人简介：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。目前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：主持国家自然科学基金面上项目、浙江省自然科学基金， 博士后基金，日本GCOE项目及参与各类基金10余项。
