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Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin function

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  • Liang, Ziwei
  • Meng, Xinyou

Abstract

In this paper, we consider a predator–prey model with fear response delay, gestation delay, fear effect, prey refuge, harvesting and Crowley–Martin type functional response. First, we discuss the model without delays and corroborate the positivity and boundedness of the solution. Then, we give some sufficient conditions for the existence and stability of three equilibriums. For the model with delays, we not only analyze the local stability of the positive equilibrium and the occurrence of Hopf bifurcation, but also obtain the crossing curves to study the stability switches of the positive equilibrium on the delays plane. Furthermore, we calculate the normal form of Hopf bifurcation and hence get the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. At last, we support our findings by numerical simulations.

Suggested Citation

  • Liang, Ziwei & Meng, Xinyou, 2023. "Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin function," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923008561
    DOI: 10.1016/j.chaos.2023.113955
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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.
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    8. Dubey, Balram & Sajan, & Kumar, Ankit, 2021. "Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 164-192.
    9. Shang, Zuchong & Qiao, Yuanhua, 2023. "Multiple bifurcations in a predator–prey system of modified Holling and Leslie type with double Allee effect and nonlinear harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 745-764.
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    Cited by:

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    2. Qingyi Cui & Changjin Xu & Wei Ou & Yicheng Pang & Zixin Liu & Peiluan Li & Lingyun Yao, 2023. "Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay," Mathematics, MDPI, vol. 11(23), pages 1-23, November.

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