Modeling and analysis of a prey-wholly dependent predator system with reserved area

Abstract

In this paper, a mathematical model for a prey-wholly dependent predator system with reserved area has been proposed and analyzed. It is assumed that the habitat consisting of unreserved area, where the predator attack its sole food the prey, and reserved area, where the prey lived safely. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions are established. Local bifurcation near the equilibrium points have been investigated. Finally numerical simulation has been used to confirm our obtained analytical results and specify the control set of parameters.