The effect of interference time in a predator–prey–nonprey system

Abstract

In this paper, we propose a three-species model consisting of two competing (prey and nonprey) species and a predator species. Here, nonprey species are not included in the predator’s food choice. The competition process follows Holling type II competitive response to interference time. Basic results include the stability of the system. First, it is established that an increasing number of interference time stabilizes the system. Second, it is shown that the interference time has an impact on the predator equilibrium density. Third, we develop the criterion of persistence of all the species. It is also shown that the system may not be persistent when multiple steady states appear. We examine the global stability of the coexistence equilibrium point. Numerical experiments are carried out to understand the analytical outcomes.