Abstract:

Species ecology systems are often subject to environment white noises. Because of this result, a prey-predator system with random perturbation is investigated, which is also based on a modified version of the Lesile-Gower and Holling Ⅱ schemes with time delay. By applying a comparison theorem for stochastic differential equations and It’s formula, a unique positive global solution and its pth moment’s upper bound are obtained respectively. And then its global symptotical stability is proved by constructing Lyapunov functional. Finally, two types of numerical simulations, state portrait and phase portrait, are presented to illustrate the correctness of the proposed theory.