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

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

2011-05-19

arxiv.org/abs/1105.3913v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

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.

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