Effects of additional resource and degeneracy on the dynamics for a diffusive predator-prey system

Abstract

A predator-prey system with Holling-II functional response in the presence of additional food resource and degeneracy is proposed in this paper. The main objective is to show the effects of additional food resource and degeneracy on the dynamics for system. We mainly obtain that there exist two critical values induced by degeneracy and improved functional response respectively, such that the system permits positive solutions. Additionally, we also show that both providing additional resource to predator with high quantity or quality, and introducing degeneracy effect into system have positive impacts in improving the amount of predator, which is indeed an environmentally-friendly strategy in preserving biodiversity.