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Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour

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  • Zhenglong Chen

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Shunjie Li

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

  • Xuebing Zhang

    (School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China)

Abstract

This paper is devoted to studying the dynamics of a delayed reaction-diffusion predator–prey system incorporating the effects of fear and anti-predator behaviour. First, based on its mathematical model, the global attractor is analyzed and the local stability of its positive equilibria is derived. Moreover, the Hopf bifurcation induced by the time delay variable is also investigated. Furthermore, the existence and non-existence of non-constant positive solutions are analyzed. Finally, numerical simulations are presented to validate the theoretical analysis.

Suggested Citation

  • Zhenglong Chen & Shunjie Li & Xuebing Zhang, 2022. "Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3270-:d:910389
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    References listed on IDEAS

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    1. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    2. Yang, Ruizhi & Ma, Jian, 2018. "Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 128-139.
    3. 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.
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