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<p>This paper studies the existence and bifurcation structure of steady-state solutions for a diffusive prey–predator model incorporating prey taxis and an Allee effect in the predator population, subject to homogeneous Dirichlet boundary conditions. Using the predator’s growth rate as the bifurcation parameter, we employ global bifurcation theory to establish a connected branch of positive steady states linking two semitrivial solutions. Our analysis provides explicit parameter ranges guaranteeing the existence of these non-trivial steady states, offering new insights into the model’s dynamical behavior.</p>

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Global steady-state bifurcation in a diffusive prey–predator model with prey taxis and Allee effect

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Hong Liang,
  • Shanbing Li

摘要

This paper studies the existence and bifurcation structure of steady-state solutions for a diffusive prey–predator model incorporating prey taxis and an Allee effect in the predator population, subject to homogeneous Dirichlet boundary conditions. Using the predator’s growth rate as the bifurcation parameter, we employ global bifurcation theory to establish a connected branch of positive steady states linking two semitrivial solutions. Our analysis provides explicit parameter ranges guaranteeing the existence of these non-trivial steady states, offering new insights into the model’s dynamical behavior.