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Turing, Hopf and Turing–Hopf bifurcations in a modified Leslie–Gower predator–prey diffusive system with Smith prey growth and nonmonotonic functional response

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  • Li, Lu
  • Yan, Xiang-Ping
  • Zhang, Cun-Hua

Abstract

A modified Leslie–Gower predator–prey reaction–diffusion system with prey growth of Smith type and nonmonotonic functional response function and subject to homogeneous Neumann boundary condition is concerned in this paper. Various bifurcations including Hopf bifurcation, Turing bifurcation and Turing–Hopf bifurcation of the unique positive constant equilibrium are analyzed in detail. In the absence of the effect of diffusion, the local stability, the existence and properties of Hopf bifurcation of the unique positive equilibrium of the corresponding ODE system are discussed deeply and the associated theoretical results are also verified numerically. In the stable domain of the positive equilibrium the corresponding ODE system, Turing bifurcation and spatially homogeneous Hopf bifurcation of the positive constant equilibrium of the original reaction–diffusion system are investigated including existence, normal form and numerical verifications. Meanwhile, Turing–Hopf bifurcation reflecting the interaction of spatially homogeneous Hopf bifurcation and Turing pattern like eigenfunction corresponding to the principle eigenvalue of −Δ subject to homogeneous Neumann boundary condition is also studied.

Suggested Citation

  • Li, Lu & Yan, Xiang-Ping & Zhang, Cun-Hua, 2025. "Turing, Hopf and Turing–Hopf bifurcations in a modified Leslie–Gower predator–prey diffusive system with Smith prey growth and nonmonotonic functional response," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012391
    DOI: 10.1016/j.chaos.2025.117226
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    References listed on IDEAS

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    1. Feng, Xiaozhou & Liu, Xia & Sun, Cong & Jiang, Yaolin, 2023. "Stability and Hopf bifurcation of a modified Leslie–Gower predator–prey model with Smith growth rate and B–D functional response," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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    3. Li, Peiluan & Gao, Rong & Xu, Changjin & Ahmad, Shabir & Li, Ying & Akgül, Ali, 2023. "Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Han, Xiaoling & Lei, Ceyu, 2023. "Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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