Mathematical Biology Seminar Abstract
Apr 9, 2019
Ting-Hao Hsu
University of Miami, Department of Mathematics
10:30 am in MSB 318

A criterion of the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model

Relaxation oscillations are periodic orbits formed from slow and fast sections. In this talk, we start with the classical predator-prey system with small predator death rates, and derive characteristic functions that determine the location and the stability of relaxation oscillations. Then we extend the criterion (joint work with Gail Wolkowicz) to a class of planar systems with application to an epidemic model. Finally, we further extend the criterion (joint work with Shigui Ruan) to systems with multi-dimensional slow variables to study rapid evolution in predator-prey interactions.