The Bifurcation of Stage Structured Prey-Predator Food Chain Model with Refuge

In this paper, we established the condition of the occurrence of local bifurcation (such as saddlenode, transcritical and pitchfork)with particular emphasis on the hopf bifurcation near of the positive equilibrium point of ecological mathematical model consisting of prey-predator model involving prey refuge with two different function response are established. After the study and analysis, of the observed incidence transcritical bifurcation near equilibrium point ????0 ,????1 ,????2 as well as the occurrence of saddle-node bifurcation at equilibrium point ????3 .It is worth mentioning, there are no possibility occurrence of the pitch fork bifurcation at each point. Finally, some numerical simulation are used to illustration the occurrence of local bifurcation o this model.