Traveling wave solutions for a predator-prey system with Sigmoidal response function
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 Dunbar1,Dunbar2. A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in 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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