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Complex dynamics of Hastings–Powell model with additive Allee effect and Crowley–Martin functional response

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  • Zhao, Tiantian
  • Han, Xiaoling

Abstract

This paper focuses on a three-trophic-level food chain model involving species mutual interference, characterized by the Crowley–Martin functional response and incorporating the Allee effect for the prey species. In addition to establishing the existence of ecologically feasible equilibria, we comprehensively analyze the positivity, boundedness, dissipativeness, and permanence of the proposed model system. The global stability of the system at the coexistence equilibrium is duly validated through a suitably constructed Lyapunov function. We also establish adequate criteria for detecting local bifurcations. Sotomayor’s theorem implies the presence of saddle–node and transcritical bifurcations. Using center manifold theory and the Hopf bifurcation theorem, we investigate the emergence and stability of limit cycles via Hopf bifurcation. Finally, numerical simulations are conducted to further analyze the effects of prey refuge, intraspecific competition and the Allee effect on population dynamics.

Suggested Citation

  • Zhao, Tiantian & Han, Xiaoling, 2025. "Complex dynamics of Hastings–Powell model with additive Allee effect and Crowley–Martin functional response," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925004448
    DOI: 10.1016/j.chaos.2025.116431
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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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    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.
    4. Pal, Pallav Jyoti & Saha, Tapan, 2015. "Qualitative analysis of a predator–prey system with double Allee effect in prey," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 36-63.
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