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<p>This paper focuses on the qualitative analysis of the diffusive Monod–Haldane predator-prey model with Smith growth rate under Neumann boundary condition. First, the stability of the solution of corresponding ODE system is studied, and then the Hopf divergence direction and the stability of periodic solutions are given. Then considering the non-uniform distribution of populations in nature, by standard linear operator theory and center manifold theorem, the Turing instability and the Hopf bifurcation of the PDE system with diffusion effects is analyzed. Finally, the theoretical calculation results are verified by numerical simulations. It can be observed that the variation of Smith growth rate and diffusion coefficient within a certain range can increase the complexity of the model.</p>

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Stability and Hopf bifurcation of a predator-prey model with Smith growth rate and Monod–Haldane functional response

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月11日

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  • Xiaozhou Feng,
  • Kunyu Li,
  • Mengyan Liu,
  • Lin Wang,
  • Tonghui Wang

摘要

This paper focuses on the qualitative analysis of the diffusive Monod–Haldane predator-prey model with Smith growth rate under Neumann boundary condition. First, the stability of the solution of corresponding ODE system is studied, and then the Hopf divergence direction and the stability of periodic solutions are given. Then considering the non-uniform distribution of populations in nature, by standard linear operator theory and center manifold theorem, the Turing instability and the Hopf bifurcation of the PDE system with diffusion effects is analyzed. Finally, the theoretical calculation results are verified by numerical simulations. It can be observed that the variation of Smith growth rate and diffusion coefficient within a certain range can increase the complexity of the model.