Bifurcation of a Prey-predator System with Holling Type-III Functional Response Function

We consider a predator-prey system with generalized Holling type-III functional response. The results developed in this article reveal far richer dynamics compared to the model without Holling type-III functional response. The model have two equilibrium in the interior for some values of parameters. We perform a qualitative analysis of model which includes positivity of solutions local asymptotic stability and bifurcation of equilibrium and analyze the local stability properties of the equilibrium of the model through the standard linearization technique. The main purpose of the article is to offer a relatively complete mathematical analysis for the model.