Stationary distribution and extinction of a stochastic one-prey two-predator model with Holling type II functional response. Issue 3 (4th May 2019)

• Record Type: Journal Article
• Authors: Liu, Qun; Jiang, Daqing
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 3(2019)
• Page Start: 321
• Page End: 345
• Publication Date: 2019-05-04
• Subjects: Stochastic Holling II predator–prey model -- persistence -- extinction -- stationary distribution -- ergodicity; 34E10; 60H10; 92B05; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1566005
• Languages: English
• ISSNs: 0736-2994

Abstract

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.