Traveling wave solutions for a predator-prey system with Sigmoidal response function

TL;DR

This paper proves the existence of traveling wave solutions in a predator-prey model with a Sigmoidal response, using an improved Wazewski set method that simplifies previous approaches.

Contribution

It introduces a simplified Wazewski set approach for establishing traveling wave solutions in a predator-prey system with a Sigmoidal response function, extending previous methods.

Findings

Existence of traveling wave solutions connecting two equilibria.

Use of a bounded Wazewski set simplifies the proof.

Method improves upon previous unbounded set approaches.

Abstract

We study the existence of traveling wave solutions for a diffusive predator-prey system. The system considered in this paper is governed by a Sigmoidal response function which is more general than those studied previously. Our method is an improvement to the original method introduced in the work of Dunbar \cite{Dunbar1,Dunbar2}. A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in \cite{Dunbar1,Dunbar2}. The existence of traveling wave solutions connecting two equilibria is established by using the original Wazewski's theorem which is much simpler than the extended version in Dunbar's work.