Stationary distribution and extinction of a stochastic one-prey two-predator model with Holling type II functional response

Abstract

In this article, we investigate a stochastic one-prey two-predator model with Holling type II functional response. We first establish sufficient conditions for persistence and extinction of prey and predator populations, then by constructing a suitable stochastic Lyapunov function, we establish sharp sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model. The results show that the smaller white noise can ensure the persistence of prey and predator populations while the larger white noise can lead to the extinction of prey and predator populations.

Keywords:

• Stochastic Holling II predator–prey model
• persistence
• extinction
• stationary distribution
• ergodicity

MATHEMATICS SUBJECT CLASSIFICATION:

• 34E10; 60H10; 92B05

Additional information

Funding

This work was supported by the National Natural Science Foundation of P.R. China (No. 11871473), Natural Science Foundation of Guangxi Province (No. 2016GXNSFBA380006), the Fundamental Research Funds for the Central Universities (No. 15CX08011A) and KY2016YB370.