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Global stability of a delayed predator–prey system with fear and Holling-type II functional response in deterministic and stochastic environments

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  • Shao, Yuanfu

Abstract

This paper is concerned with a delayed predator–prey system where besides direct predation, the prey species are affected by fear factor induced from predator species. The globally asymptotical stability of the coexisting equilibrium state in deterministic environment is studied. By perturbing the natural growth rates of prey species and predator species, the deterministic system is then extended to a stochastic version with white noise. We investigate the existence of stochastic positive solution and globally asymptotical stability of the equilibrium state. Our main results demonstrate that the fear and delay are harmless for the global stability of the equilibrium state in some cases, but sufficiently large white noise will destroy the stability. Some numerical examples are given to verify our analytical results.

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  • 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.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:65-77
    DOI: 10.1016/j.matcom.2022.04.013
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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. Zhang, Xinhong & Li, Wenxue & Liu, Meng & Wang, Ke, 2015. "Dynamics of a stochastic Holling II one-predator two-prey system with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 571-582.
    4. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    5. Zhao, Yu & Yuan, Sanling, 2016. "Stability in distribution of a stochastic hybrid competitive Lotka–Volterra model with Lévy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 98-109.
    6. Zuo, Wenjie & Jiang, Daqing & Sun, Xinguo & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Long-time behaviors of a stochastic cooperative Lotka–Volterra system with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 542-559.
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    Cited by:

    1. 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.
    2. Yuke Zhang & Xinzhu Meng, 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance," Mathematics, MDPI, vol. 10(16), pages 1-18, August.

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