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

Author

Listed:
  • 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
    Key Laboratory of Ministry of Education for Data Science and Intelligence Education, Hainan Normal University, Haikou 571158, China
    Ministry of Education and Key Laboratory of Computational Science and Application of Hainan Province, Hainan Normal University, Haikou 571158, China)

  • Daqing Jiang

    (School of Science, China University of Petroleum (East China), Qingdao 266580, China
    Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, King Abdulaziz University, Jeddah 121589, Saudi Arabia)

  • Donal O’Regan

    (School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 TK33 Galway, Ireland)

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.

Suggested Citation

  • Quan Wang & Li Zu & Daqing Jiang & Donal O’Regan, 2023. "Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2735-:d:1172910
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    References listed on IDEAS

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    1. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    2. Zu, Li & Jiang, Daqing & O’Regan, Donal & Hayat, Tasawar & Ahmad, Bashir, 2018. "Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 93-102.
    3. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
    4. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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