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)
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.
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