The Dynamics of Prey-Predator Model with Different Types of Functional responses

In this book, A structure and dynamics of a food web prey-predator model are proposed and studied by using different types of functional responses ( Lotka-Volterra and type II functional response ) to describe the variety species' interactions in this proposed model. Age stages which are divided into two categories (mature and immature) with refuge in prey population and two predators (top and mid) are considered. The assumption of this model is that in the absence of predator the prey growth logistically, and the role of the prey refuges is the most important factor that has a negatively effect on the predator species and then lead to its extinction, this role has been investigated extensively. The existence of equilibrium points, uniqueness and boundedness of the solution of the proposed model are proven. The local dynamics and the global dynamics with the help of a suitable Lyapunov function are studied for all possible equilibrium points.