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Dynamic properties and fishing behavior analysis of a predator-prey model with carrying-over fear and Allee effects

Author

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  • Liu, Yang
  • Tian, Yuan
  • Sun, Kaibiao

Abstract

This study investigates the dynamic characteristics and fishing behavior of a fishery predator–prey model, in which the prey growth is regulated by both the Allee effect and the carrying-over fear effect. The key outcomes are as follows: First, by analyzing the bifurcation scenarios under different parameter conditions using bifurcation theory, it is revealed that the system undergoes a saddle–node bifurcation with variations in key parameters. Second, to facilitate the sustainable exploitation of fish resources, a feedback control model integrating a weighted fishing strategy is constructed. Through the application of Poincaré mapping, successor functions, and the Analogue of Poincaré criterion, the existence and stability of the order-1 and order-2 periodic solutions of the system are verified. Finally, numerical simulations are conducted, which not only validate the theoretical findings but also provide practical implications, offering a more effective method for modern fisheries management.

Suggested Citation

  • Liu, Yang & Tian, Yuan & Sun, Kaibiao, 2025. "Dynamic properties and fishing behavior analysis of a predator-prey model with carrying-over fear and Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012238
    DOI: 10.1016/j.chaos.2025.117210
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    References listed on IDEAS

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    1. Guo, Hongjian & Chen, Lansun & Song, Xinyu, 2015. "Qualitative analysis of impulsive state feedback control to an algae-fish system with bistable property," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 905-922.
    2. R. Lavanya & S. Vinoth & K. Sathiyanathan & Zeric Njitacke Tabekoueng & P. Hammachukiattikul & R. Vadivel & Kenan Yildirim, 2022. "Dynamical Behavior of a Delayed Holling Type-II Predator-Prey Model with Predator Cannibalism," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, September.
    3. Li, Yajing & He, Mengxin & Li, Zhong, 2022. "Dynamics of a ratio-dependent Leslie–Gower predator–prey model with Allee effect and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 417-439.
    4. Chen, Fengde & Li, Zhong & Pan, Qin & Zhu, Qun, 2025. "Bifurcations in a Leslie–Gower predator–prey model with strong Allee effects and constant prey refuges," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    5. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Tian, Yuan & Yan, Xinrui & Sun, Kaibiao, 2024. "Dual effects of additional food supply and threshold control on the dynamics of a Leslie–Gower model with pest herd behavior," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
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