The Dynamics of Food Web Model with Defensive Switching Property

Abstract

In this paper, a food web model consisting of two-predator one-prey with the defensive switching of predation avoidance is proposed and analyzed. It is assumed that the prey growth logistically in the absence of predators and defends itself from relatively abundant predator species by switching to another habitat with relatively rare predator species. Sufficient conditions for the stability of the non-trivial equilibrium point are obtained. The Lyapunov function is constructed to establish the global asymptotic stability of the non-trivial equilibrium point when the intensity of defensive switching equal one. Numerical simulations for different sets of parameter values and for different sets of initial conditions are carried out. It has been shown that the system has a globally asymptotically stable non-trivial point when the two predators have the same mortality rates.