Survivability and stochastic bifurcations for a stochastic Holling type II predator-prey model

In this paper, the dynamic properties of a stochastic model are studied through the stability of ergodic invariant measures on invariant sets. The threshold analysis of strong stochastic persistence and extinction is given. Moreover, the necessary and sufficient condition for persistence and extinction in the sense of time average is give for a special critical state. The stochastic bifurcation phenomenon of the model is studied from the viewpoint of dynamic bifurcation. The main conclusions are verified by examples and numerical simulations. In addition, the intra-specific competition of two species are considered in this paper, the importance of intra-specific competition is also illustrated by theoretical results. The results can also provide a theoretical basis for the modeling of stochastic population models.