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Dynamics of a diffusive predator–prey model with nonlocal fear effect

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  • Sun, Xiuli

Abstract

The fear effect on prey populations due to the presence of a predator’s sound or smell can be more impactful than direct predation. In this paper, we formulate a diffusive predator–prey model incorporating the nonlocal fear effect. The existence and boundedness of solutions are showed. We also study the stability of constant steady states by using the characteristic equation and Lyapunov functionals. Steady-state bifurcations are carried out in detail by the Lyapunov-Schmidt method. The analyses demonstrate that the fear effect in the system can change the stability of the constant steady state and there exist spatially nonhomogeneous steady states. Hopf bifurcations are also investigated and the results show that high levels of fear can stabilize the model by excluding the existence of periodic solutions. Finally, numerical simulations are sketched to illustrate our theoretical findings. This work can help us further understand the impact of fear effect on the stability of constant steady states, steady-state bifurcations and Hopf bifurcations of predator–prey models.

Suggested Citation

  • Sun, Xiuli, 2023. "Dynamics of a diffusive predator–prey model with nonlocal fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011232
    DOI: 10.1016/j.chaos.2023.114221
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    1. Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar, 2021. "Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. 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.
    3. Duan, Daifeng & Niu, Ben & Wei, Junjie, 2019. "Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 206-216.
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