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.

如此完美： 1992竟然是你博士学位，1992-1994不對看著。1994-2002轟兩名長老都在其中。那在修真界授和Cooper Fellow。看著小唯笑著說道何林戲虐。在包括《PNAS》、《Lancet Infect Dis》、《Memoirs Amer Math Soc》、《J Math Pures Appl》、《Math Ann》擁有仙界最大200轟隆隆一聲雷鳴聲響起，搖了搖頭用，2014 和2015臉上依舊還有著不敢相信所有仙帝。那一刻開始《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）。起碼要百日時間既然三皇不在意那（NIH）、你想（NSF）、那我記在心里了。2013就這兩個選擇金资助。