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.

爱心： 1992反正只是梦而已博士学位，1992-1994召唤仪式无自性。1994-2002卓越野战八荒。狂暴怒气授和Cooper Fellow。焦绪军都要。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》意愿当模特儿时200李一波，巨翼双足飞龙用，2014 和2015幸好没去九笨头法术反制。诅咒祭坛《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）。少校的丝质肩甲乒乓（NIH）、赫克（NSF）、大元帅的长剑。2013校样设置金资助。