Stability Of A Modified Leslie-Gower Predator-Prey Model With Crowley-Martin Functional Response

In this paper,we are concerned with the stability of a modified Leslie-Gower predator-prey model with Crowley-Martin functional response.The whole thesis is mainly make up of two parts.In the first part,we investigate the following modified Leslie-Gower predatorprey model with Crowley-Martin functional response By using linearization method,we prove the stability of nonnegative equilibrium points;and we obtain the existence,direction and stability of Hopf bifurcations by using Poincare-Andronov-Hopf bifurcation theorem.In the second part,we consider the following the semi-linear reaction-diffusion model Firstly,we prove the stability of the non-negative equilibrium points by using the linearization method.Secondly,we study the global asymptotic stability of the unique positive equilibrium solution of the model by iteration method and Lyapunov function method,respectively.Finally,the Turing instability of the model is discussed.