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.
Highlights
In predator-prey environment, there is variety of ways in which potential prey attempts to avoid predators; these anti-predator behaviors include habitat selection, vigilance and other types of behaviors [1,2,3,4]
In the last two decades number of papers have been done on the effects of switching mechanism of prey and / or predator, due to variety of biological concepts, on the behavior of population dynamics [11,12,13,14,15,16,17,18]
The effect of optimal diet choice in two-prey-onepredator population dynamic model is investigated in Krivan [11]
Summary
In predator-prey environment, there is variety of ways in which potential prey attempts to avoid predators; these anti-predator behaviors include habitat selection, vigilance and other types of behaviors [1,2,3,4]. If each of the different behaviors is effective against all predator species it is perfectly non-specific defense [5]. Bifurcation analysis was used to study the effect of switching, as regulated by CRCL, on the dynamics and survival of both prey and predator populations. Saleem et al [5] analyzed a mathematical model consisting of two-predator feeding on a single prey has defensive switching property for predation avoidance. They assumed that the prey is growing exponentially in the absence of predators. The effect of prey’s defensive switching on the dynamical behavior of the food web model is investigated theoretically as well as numerically
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