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

Yuwei Shen, Zhihong Zhao and Ke Guo

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

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.

Keywords: Prey refuge; Ratio-dependence; Hopf bifurcation; Turing instability; Turing–Hopf bifurcation (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925008252

DOI: 10.1016/j.chaos.2025.116812

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