Traveling Wave Solutions for a Predator– Prey System With Sigmoidal Response Function

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 in some applications is more realistic than the Holling type I, II responses, and more general than a simplified form of the Holling type III response considered before. Our method is an improvement to the original method introduced in the work of Dunbar (J Math Biol 17:11–32, 1983; SIAM J Appl Math 46:1057–1078, 1986). A bounded Wazewski set is used in this work while unbounded Wazewski sets were used in Dunbar (1983, 1986). 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.