Abstract: The main goal of this research is to formulate a time-continuous model by considering the reaction-diffusion model as systems of ODE, which describe three types of predator-prey model living in a habitat of two identical patches linked by migration: 1- Predator-prey of Holling Type II . 2- Predator-prey of Holling-Tanner Type. 3- Predator-prey of Beddington- DeAngelis and Type. In this research, we study the conditions of the existence and stability properties of the equilibrium solutions in both kinetic model (with no diffusion) and the model with diffusion. This allows us to explore the effect of diffusion on the stability of the equilibrium solutions.