时间 Datetime
2021-06-09 09:30 — 10:30
地点 Venue
腾讯会议 APP3()
报告人 Speaker
Prof. Shigui Ruan
单位 Affiliation
Department of Mathematics, University of Miami, USA
邀请人 Host
肖冬梅
备注 remarks
腾讯会议 ID: 659 924 850, Password：210609
报告摘要 Abstract
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 shorter lifespan than hosts (humans); some species exhibit more rapid evolution, and so 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. (Based on a joint paper with Ting-Hao Hsu).
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