Persistence, spreading speeds and traveling waves for evolution systems in biology

Dr. Xiaoqiang Zhao

Memorial University of Newfoundland and Georgia Institute of Technology

November 18, 2005
202 Madison Hall
3:30 PM (Coffee and Cookies at 3:00)

Abstract

The conjoining of nonlinear dynamics and biology has brought about significant advances in both areas, with nonlinear dynamics providing a tool for understanding biological phenomena and biology stimulating developments in the theory of dynamical systems. Various evolution equations arise naturally in many areas in the biological sciences, and a fundamental problem is to study the evolutionary (long-term) behavior of these systems. For example, people expect to answer whether and how a community of interacting populations can persist (avoid extinction) or whether an infectious disease becomes endemic in a population, and to understand spatial-temporal patterns and speeds of biological invasion or disease spread.

In this talk, I will first introduce the dynamical systems approach and the concepts of uniform persistence, traveling waves and spreading speeds. Then I will give a brief review on the related mathematical theory and methods. Finally I will discuss their applications to some deterministic models from population biology and epidemiology.