Multiple Periodicity in a Predator-PreyModel with Prey Refuge

Abstract

We consider a delayed prey-predator model incorporating a refuge with a non-monotone functional response. It is supposed that prey can live in the predatory region and prey refuge, respectively. Based on Mawhin’s coincidence degree and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation Lυ = λNυ, we prove the existence of multiple periodic solutions. Finally, an example demonstrates the feasibility of our main results.