The prey predator interaction is fundamental and important process in a population dynamic. In this paper, a diffusive prey predator holling type II model considering limitation of the prey growth is presented. The model consists two distinct populations. Model is a nonlinear system of partial differential equations which is a initial boundary value problem. The behaviour solution of the model was analyzed by analyzing stability of the critical point. In solving this system, we use Homogeneous Neumann boundary conditions. Numerical solution was determined by using finite difference method. The results show that the diffusive model illustrates a spreading population over a limited area.

A prey predator model which consists of two distinct population is discussed. The model used Holling response function of type II without limiting on prey population growth. Equilibrium points of the model was determined and stability of the model was analyzed by phase plane analysis. Furthermore, the model is reformulated by adding a diffusive terms to understand the spatial effect of the dynamical system behaviour. Solutions of the diffusive model were numerically illustrated with Neumann boundary conditions. Numerical simulations are presented to confirm the analytical results.