Bifurcation and Stability Analysis in Dynamics of Prey-Predator Model with Holling Type IV Functional Response and Intra-Specific Competition

This paper deals with the dynamical behaviour of discrete Prey-Predator model with Holling type IV involving intra-specific competition. This model represents mathematically by nonlinear differential equations. The existence, uniqueness and boundedness solutions of this model were investigated. The locally asymptotic stability conditions of all possible equilibrium points were obtained. The stability/instability of nonnegative equilibria and associated bifurcation are investigated by analyzing the characteristic equations. Moreover, bifurcation diagram are obtained for different values of parameters of this model. Finally, numerical simulation was used to study the global and rich dynamics of this model.