Global dynamics and bifurcation of a tri-trophic food chain model

This paper deals with the dynamics of a tritrophic food chain model composed of a prey, predator and a super predator. A discrete time delay is introduced to the functional response term involved with the growth equation of predator and super predator to allow for a reaction time. The main content of this paper is divided into two parts. In the first part we consider the model with density dependent mortality terms for the predator and the super predator and in the second part we consider the model without density dependent mortality terms. In the first part we analyzed the global stability of the interior equilibrium and the boundary equilibrium points by using a suitable Lyapunov function and the Hopf bifurcations of the model with respect to the delay parameter. In the second part of the paper, equilibrium points are obtained and bifurcation is done with respect to two model parameters. Computer simulations are given to verify most of the analytical results.