Density dependent mortality and weak Allee effect control chaos-conclusion drawn from a tri-trophic food chain with prey refugia

Abstract

In this article, we explore the Hasting-Powell's tri-trophic food chain model with prey refugia, and prey species subject to the weak Allee effect. We consider a prey-predator model with Holling type II functional response and density-dependent mortality of intermediate predator. We perform the local stability analysis of the system around the biologically feasible equilibria and the Hopf bifurcation analysis of the system around interior equilibrium point. Our analytical and supporting numerical results reveal that the tri-trophic food chain model induced chaos from stable focus for increasing the half-saturation constant, where as density-dependent intermediate predator mortality can stabilize chaotic dynamics of the model. The weak Allee effect and refugia also controlling chaotic nature of prey-predator system and promote to stabilize the coexistence of all species in a prey-predator system.