Sample Sidebar Module

This is a sample module published to the sidebar_top position, using the -sidebar module class suffix. There is also a sidebar_bottom position below the menu.

Sample Sidebar Module

This is a sample module published to the sidebar_bottom position, using the -sidebar module class suffix. There is also a sidebar_top position below the search.
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Abstract

In this paper, a food chain model consisting of mid- predator and top predator – stage structhred prey involving two functional response Lotka-Voltera type and Holling type – II with a prey, is proposed and analyzed.For this model , 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 stability analysis of all possible equilibrium points are studied . Suitable Lyapunov functions are used to study the global dynamics of the proposed model.Finally, numerical simulation for different sets of parameter value and for different sets of initial conditions are carried out to investigate the influence of parameters ouon the dynamical behavior of the model and to support  our obtained analytical results of the model.