Traveling wave solutions for a predator-prey system with Sigmoidal response function
Pattern Formation and Solitons
2015-05-28 v1
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.
Keywords
Cite
@article{arxiv.1105.3913,
title = {Traveling wave solutions for a predator-prey system with Sigmoidal response function},
author = {Xiaobiao Lin and Peixuan Weng and Chufen Wu},
journal= {arXiv preprint arXiv:1105.3913},
year = {2015}
}