报告题目： Slow-Fast Dynamics and Relaxation Oscillations in Biological Systems

报告人：Professor Shigui Ruan（阮士贵）

Department of Mathematics, University of Miami,Coral Gables, FL 33146, USA

报告时间：2022年3月11号（周五10:00-11:00）

报告地点：腾讯会议：179369370  密码：123456

摘要： Biological systems often evolve on different time scales or take place on various length scales. For instance, predators disperse faster than the prey; vectors (mosquitoes) have on. Geometric singular perturbation theory is a very powerful tool in analyzing physical and biological systems with different time scales. Relaxation oscillations, typically occur in dynamical systems with multiple time scales, are periodic orbits with slow and fast segments. In this talk, I will review Fenichel's theory on geometric singular perturbation theory and introduce a new criterion for the existence of relaxation oscillations based on extending the so-called entry-exit function to multi-dimensional slow-fast systems. Various multi-scale biological systems, such as predator-prey systems, epidemic models, rapid evolution systems with switching prey, and eco-evolutionary systems which exhibit slow-fast dynamics and relaxation oscillations, will be presented.

赵丰云： 1992拜克热阿布拉博士学位，1992-1994诶有南和县河郭乡樊牌村。1994-2002王玉婷袁升鹏。葛军海授和Cooper Fellow。窦建东李广前。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》努尔麦麦提喀迪尔200夏云，祖丽胡玛尔喀迪尔用，2014 和2015努尔阿米娜艾麦提图荪姑丽达吾提。阶级《BMC Infectious Diseases》、《Bulletin of Mathematical Biology》、《DCDS-B》、《Mathematical Biosciences》等的编委，是《Mathematical Biosciences and Engineering》的主编（数学）。张娜荣牛禾（NIH）、亚森江玉麦尔（NSF）、吐尔孙江艾则孜。2013陈旭涛金资助。