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Bifurcations and pattern formation of a ratio-dependent Holling–Tanner predator–prey model with prey refuge

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  • Shen, Yuwei
  • Zhao, Zhihong
  • Guo, Ke

Abstract

This paper explores a ratio-dependent Holling–Tanner predator–prey model incorporating prey refuge. We first analyze the impact of prey refuge on the stability and Hopf bifurcation at positive equilibrium in the non-spatial system. Subsequently, we explore the joint effects of prey refuge and diffusion ratio on stability and spatio-temporal dynamics , which demonstrate rich dynamical behavior through the Turing bifurcation and the Turing–Hopf(TH) bifurcation. The normal form on center manifold and TH bifurcation diagrams are derived via reaction–diffusion normal form theory. Finally, we provide numerical studies of non-spatial system and diffusion system near positive equilibrium to verify the theoretical analysis.

Suggested Citation

  • Shen, Yuwei & Zhao, Zhihong & Guo, Ke, 2025. "Bifurcations and pattern formation of a ratio-dependent Holling–Tanner predator–prey model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925008252
    DOI: 10.1016/j.chaos.2025.116812
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    References listed on IDEAS

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    1. Zhao, Zhihong & Shen, Yuwei, 2025. "Dynamic complexity of Holling-Tanner predator–prey system with predator cannibalism," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 227-244.
    2. 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).
    3. Barman, Dipesh & Roy, Jyotirmoy & Alrabaiah, Hussam & Panja, Prabir & Mondal, Sankar Prasad & Alam, Shariful, 2021. "Impact of predator incited fear and prey refuge in a fractional order prey predator model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Mondal, Santana & Khajanchi, Subhas, 2025. "Can adaptive prey refuge facilitate species coexistence in Bazykin’s prey–predator model?," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 539-552.
    5. Mandal, Gourav & Guin, Lakshmi Narayan & Chakravarty, Santabrata & Han, Renji, 2025. "Dynamic complexities in a predator–prey model with prey refuge influenced by double Allee effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 527-552.
    6. Guin, Lakshmi Narayan & Djilali, Salih & Chakravarty, Santabrata, 2021. "Cross-diffusion-driven instability in an interacting species model with prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    7. Mondal, Bapin & Ghosh, Uttam & Sarkar, Susmita & Tiwari, Pankaj Kumar, 2024. "A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 968-991.
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