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A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments

Author

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  • Yuanfu Shao

    (School of Science, Guilin University of Technology, Guilin 541004, China)

  • Weili Kong

    (School of Teacher Education, Qujing Normal University, Qujing 655011, China)

Abstract

In view of prey’s delayed fear due to predators, delayed predator gestation, and the significance of intra-specific competition between predators when their populations are sufficiently large, a prey–predator population model with a density-dependent functional response is established in a deterministic environment. We research the existence and asymptotic stability of the equilibrium statuses. Then, taking into consideration environmental disturbances, we extend the deterministic model to a stochastic model and research the existence and stationary distributions of stochastic solutions. Finally, we perform some numerical simulations to verify the theoretical results. Numerical examples indicate that fear, delays and environmental disturbance play crucial roles in the system stability of the equilibrium status.

Suggested Citation

  • Yuanfu Shao & Weili Kong, 2022. "A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments," Mathematics, MDPI, vol. 10(18), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3378-:d:917350
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    References listed on IDEAS

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    1. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    2. Liu, Qun, 2015. "The effects of time-dependent delays on global stability of stochastic Lotka–Volterra competitive model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 108-115.
    3. Shao, Yuanfu, 2022. "Global stability of a delayed predator–prey system with fear and Holling-type II functional response in deterministic and stochastic environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 65-77.
    4. Weili Kong & Yuanfu Shao & Kolade M. Owolabi, 2022. "The Long Time Behavior of Equilibrium Status of a Predator-Prey System with Delayed Fear in Deterministic and Stochastic Scenarios," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, June.
    5. Xu, Dongsheng & Liu, Ming & Xu, Xiaofeng, 2020. "Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
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    Cited by:

    1. Jaouad Danane & Delfim F. M. Torres, 2023. "Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species," Mathematics, MDPI, vol. 11(7), pages 1-22, March.
    2. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review," Sustainability, MDPI, vol. 15(16), pages 1-23, August.

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