On the Dynamics of some Prey-Predator Models with Holling Type-IV Fun

The dynamical behavior of prey-predator models with non-monotonic functional response. Two types of prey-predator models are proposed and studied. The first model consisting of Holling type-IV prey predator model involving intra-specific competition in predator population. However, the second model consisting of Holling type-IV preypredator model involving intra-specific competition in predator population with stage structure in predator. Both the models are represented mathematically by nonlinear differential equations. The existence, uniqueness and boundedness of the solution of these two models are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation (such as saddle-node, trans-critical and pitchfork) and Hopf bifurcation near each of the equilibrium points are discussed. Finally, numerical simulation is used to study the global dynamics of both the models.