Existence of periodic solutions in predator–prey with Watt-type functional response and impulsive effects

Abstract

In this paper, the existence of a periodic solution and the permanence of a periodic Watt-type predator–prey system where the prey disperses in patchy environment with two patches are investigated. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. We assume the Watt-type functional response within-patch dynamics and provide a sufficient condition to guarantee the predator and prey species to be permanent. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful to ecosystem control.