Abstract
In this paper, a food web model consisting of two predator-one stage structured prey involving Lotka-Voltera type of functional response and a prey refuge , is proposed and analyzed. It is assumed that the prey growth logistically in the absence of predator. The role of prey refuges in predator-prey model is investigated. The existence , uniqueness and boundedness of the solution are studied. The existence and the stability analysis of all possible equilibrium points are studied. Suitable Lyapunov functions are used to study the global dynamics of the proposed model. Numerical simulation for different sets of parameter value and for different sets of initial conditions are carried out to investigate the influence of parameters on the dynamical behavior of the model and to support the obtained analytical results of the model .
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