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

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.

► The role of predator interference and normalization of the residual reduction is described.
► We demonstrate how the demerit of Leslie model can be removed.
► The model combines both the formulations of predator–prey interaction in a single model.
► Bifurcation diagrams and the largest Lyapunov exponent are used to detect and quantify chaos.
► Predator interference and residual reduction parameters have opposite effects on the stability.