The Study Of Stochastic Predator Prey System With Refuge Effect

In order to study the influence of random disturbance to the predator system with protective effect on the prey,considering the factors such as functional response and stage structure,the methods of stochastic differential equations such as ecology and It? formula,Lyapunov function and Chebyshev inequality were used to study the stochastic predator-prey system.The behavioral characteristics of the solution,the following results:(1)In the deterministic system of Beddington-DeAngelis(BD)type functional response,considering the refuge effect and random disturbance factors,a stochastic predator-prey system model with refuge effect and BD type functional response is established,and the behavioral characteristics of the solution are discussed.The stochastic final boundedness of the system solution,the existence and uniqueness of the global positive solution and the sufficient conditions for the global random asymptotic stability of the positive equilibrium point are obtained.(2)In the deterministic system of Crowley-Martin(CM)type functional response,considering the refuge effect and random disturbance factors,a stochastic predator system model with refuge effect and CM type functional response is established,and the stochastic final boundedness of the system solution is studied.The existence and uniqueness of the global positive solution,the global random asymptotic stability of the positive solution and the asymptotic behavior of the solution are studied.(3)A stochastic predator system with a bait is established.The adult bait has a stage structure and a refuge effect.Considering the refuge effect and random disturbance factors,the characteristics of the solution are analyzed.The existence and uniqueness of the global positive solution and the stochastic final boundedness of the solution are obtained.And sufficient conditions for global random asymptotic stability of positive equilibrium points under certain conditions are obtained.