The Dynamics of a Reaction-Diffusion Equation with Time Delay

Wenzhang Huang

Department of Mathematical Sciences
University of Alabama in Huntsville

August 20, 1996

Abstract

We consider a reaction -diffusion equation with time delay that serves as the model for some classes of population dynamics. It has been shown that the oscillation may occur if the magnitude of time delay effect is greater than the instant effect. However, it is not clear about the global dynamics (except the local stability has been observed) if the instant effect dominates the time delay effect. By a careful study of the behavior omega-limit sets of the orbits, in this talk we will give a complete characterization of the global dynamics of the model when the magnitude of time effect is dominated by the instant effect.