Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching

Quan Wang, Li Zu (), Daqing Jiang and Donal O’Regan
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Quan Wang: College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
Li Zu: College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
Daqing Jiang: School of Science, China University of Petroleum (East China), Qingdao 266580, China
Donal O’Regan: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 TK33 Galway, Ireland

Mathematics, 2023, vol. 11, issue 12, 1-17

Abstract: In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient conditions of the strong persistence in the mean and extinction were established and the threshold between them was obtained. Moreover, we took stability into account and, by means of structuring a suitable Lyapunov function with regime switching, we proved that the stochastic system has a unique stationary distribution. Finally, numerical simulations were used to illustrate our theoretical results.

Keywords: stochastic predator–prey model; Beddington–DeAngelis functional response; regime switching; persistence in the mean; stationary distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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