# Traveling Wave Solution and Principle of Competitive Exclusion

## Dr. Wenzhang Huang

### Department of Mathematical SciencesUniversity of Alabama in Huntsville

September 10, 1999

## Abstract

For a system of reaction-diffusion equations with time delay that describes the dynamics of competition models, the property of "positive limit set" associated to a bounded solution is investigated. The positive limit set is defined in a similar way as the omega limit set of a solution with an additional restriction. In the case where the nonlinear reaction term is bistable and monotone, we show that a traveling wave solution can be identified from the limit set by studying the spectrum of the corresponding variational operator. The approach introduced in this talk is new and the result obtained matches well with the principle of competitive exclusion.