Periodic solution and stationary distribution for stochastic predator-prey model with modified Leslie-Gower and Holling type II schemes

Abstract

In this paper, a stochastic predator-preysystem with modified Leslie-Gower and Holling type II schemes is studied. For the autonomous case,we prove that the system has a stationary distribution under some parametric restrictions. We also obtain conditions for the non-persistence of the system, and the results are illustrated by computer simulations. For the non-autonomous system with continuous periodic coefficients, sufficient conditions which guarantee theexistence of periodic solution of the system are established.