The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

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We proposed and analyzed a mathematical model dealing with two species of prey-predator system.It is assumed that valentines bear value psx the prey is a stage structure population consisting of two compartments known as immature prey and mature prey.It has a refuge capability as a defensive property against the predation.The existence, uniqueness, and boundedness of the solution of the proposed model are discussed.All the feasible equilibrium points are determined.

The local and global stability analysis of them are investigated.The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each hobbit door for sale of the equilibrium points is studied.Finally, numerical simulations are given to support the analytic results.