报告题目【Dynamics of the predator-prey model with the Sigmoid functional response】
时间：2020年11月24日下午14: 00
地点：腾讯会议（会议号：468 613 429）
主讲：上海交通大学特聘教授、博士生导师，张祥
主办：数学与信息学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）
参加对象：相关研究方向的老师和学生
报告摘要: For the predator-prey model with the Sigmoid functional response, the known result is on the global stability of its positive equilibrium when it is locally stable. Here we characterize its global dynamics using qualitative theory and geometric singular perturbation methods. The main results are the following.
If the positive equilibrium exists and is a weak focus, it is a stable weak focus of order 1. The positive equilibrium is unique, and it is either globally stable or unstable and there exists a limit cycle surrounding it. The limit cycle could be a canard cycle without head, or a canard cycle with head, or a relaxation oscillation. The system could present canard explosions consecutively two times, which first birthes from one canard point, via relaxation oscillation for a large range of parameter values, and then there exhibits an inverse canard explosion and disappears at another canard point with the parameter variation
报告人简介：张祥，上海交通大学特聘教授（享受国务院特殊津贴，二级教授、博导），主要从事动力系统的定性、分支和可积理论的研究。所得结果部分发表在American J. Math. Transactions of Amer. Math. Soc., Communications Math. Phys., J. Functional Analysis, J. Nonlinear Sciences 和 J. Differential Equations等国际一流数学杂志上。多次应邀在欧美举行的动力系统国际会议上做大会特邀报告。目前担任中国数学会奇异摄动专业委员会主任，中国数学会理事，以及国际SCI杂志《Qualitative Theory of Dynamical Systems》和《International J. Bifurcation and Chaos》的Associate编委等。
