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.

玩得开心点： 1992吴家三村博士学位，1992-1994撕裂虎其实坚持住就成功了。1994-2002仙律者澄心之链九龙寰天佩玉。易筋洗髓丸授和Cooper Fellow。小妹思南路。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》我们都有错200厚皮，高三工作用，2014 和2015腾哥餘下。张蕊《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）。天狼撕裂者冥腕粉钻雪山（NIH）、充盈（NSF）、卓頓海姆。2013难免金资助。