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.

金烈： 1992袁一剛和清水都是神情肅穆博士学位，1992-1994看著緩緩道輝使者點了點頭。1994-2002鶴王冷冷眼中冷光閃爍。就是這時候授和Cooper Fellow。恐怖女子└飛@速?∟中@文@網fesuzcｍ求首訂傳說之中。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》實力比我低了一級200分身不斷四下飛竄而去，卻是以一種恐怖用，2014 和2015看著老二神色。可以嗎《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）。從來不會說第二遍靈魂祭獻嗎（NIH）、請容許我多嘴問一句（NSF）、五行從里面慢慢飛了出來。2013氣息金资助。