Dynamics Of A Stochastic Cooperative Predator-Prey System With Beddington-DeAngelis Functional Response

In mathematical biology, the deterministic systems has long been a dominant theme. However, in the realistic nature, population system is inevitably affected by environmental perturbation. The stochastic system can describe the growth of population more accurately. In this paper, a stochastic cooperative predator-prey system with Beddington-DeAngelis functional response is studied.For the stochastic autonomous predator-prey system with Beddington-DeAngelis functional response, we demonstrate the existence of global positive solution by constructing Lyapunov functions, which is stochastically bounded and permanent. In addition, under some speci?c conditions, the solution of this stochastic system is globally asymptotically stable, which means that the properties of the solution will not be changed when the stochastic perturbation is small. However, when the environmental perturbation is large enough, it will lead the extinct of partial or all species of the system. Finally, the in?uence of the stochastic perturbation is demonstrated by simulation.For the stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response, when parameters of system are the bounded positive function of time t, the long-time dynamic behavior of the stochastic system is given. According to stochastic differential equation Comparative method, we obtain a estimation of the solution.Then showing moment boundedness of solution, stochastic ultimate boundedness of solution can be derived. At the same time, the su?cient conditions for the permanence and extinction of the system are also obtained. In the ?nal part, numerical simulations are given to verify our conclusions.