The role of top predator interference on the dynamics of a food chain model

Abstract

In this paper, the effects of top predator interference on the dynamics of a food chain model involving an intermediate and a top predator are considered. It is assumed that the interaction between the prey and intermediate predator follows the Volterra scheme, while that between the top predator and its favorite food depends on Beddington–DeAngelis type of functional response. The boundedness of the system, existence of an attracting set, local and global stability of non-negative equilibrium points are established. Number of the bifurcation and Lyapunov exponent bifurcation diagrams is established. It is observed that, the model has different types of attracting sets including chaos. Moreover, increasing the top predator interference stabilizes the system, while increasing the normalization of the residual reduction in the top predator population destabilizes the system.