Stochastic Permanence Analysis Of Predator-prey Ecosystem Model

The confirm models have been studied by lots of reseachers, But in real world, the species can’t live without other factors, so it’s very important to study the stochastic model. In this paper, we’ve studied the persistence and extinction, via the determined theory of differential equation, and using the exponential martingale inequality and so on. The main construction of this paper is as following:In Section 3 we study a delay prey-predator system with random perturbations. Under a simple assumption, the conditions for stability in time average and extinction of each population are established. The critical value between stability in time average and extinction is obtained. And numerical simulations are introduced to support the main results.Section 4 presents the almost sufficient conditions for stability in time average and extinction of an autonomous stochastic competitive system. Finally, numerical simulations are introduced to support the main results by MATLAB.In Section 5 we study the extinction and persistence of a stochastic non-autonomous ratio-dependent predator-prey model with delay. Sufficient conditions for extinction, non-persistence in the mean and weak persistence are established. And also, numerical simulations are illustrated to confirm our main results.