An Introduction to Traveling Waves in Biological Systems

讲座时间 Datetime: 2022年7月9日，星期六，9:00—10:30

地点 Venue: 腾讯线上会议：423-680-201

主持人 Host：唐德

报告人 Speaker: 阮士贵

单位 Affiliation:美国迈阿密大学

报告摘要 Abstract:

This is an introductory talk about basic concepts, methods and results on traveling waves in biological systems described by one and two reaction-diffusion equations. For scalar biological models, traveling waves in Fisher equation (diffusive logistic equation), Fisher-KPP equation, Nagumo equation (scalar equation with Allee effect), and spruce budworm outbreak model will be introduced. For traveling waves in two-dimensional systems, we will review some results on predator-prey models, competition models, tumor growth models, FitzHugh-Nagumo nerve conduction model, and wound healing models. Methods used to study the existences and stability of traveling waves, such as phase portrait analysis, squeezing method, shooting argument, fixed point theorem, geometric singular perturbation approach, Evans function, and topological approach will be briefly explained.  Some of our recent studies on traveling waves in time-dependent biological models will also be mentioned.