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<p>This study investigates a modified Leslie–Gower predator–prey model incorporating an Allee effect in the predator population. We establish the existence and local stability of biologically feasible equilibria, prove the positivity and boundedness of solutions, and analyze bifurcation dynamics, including Hopf and Bogdanov–Takens (codimension-two) bifurcations around the positive equilibrium. The diffusive version of the model is further examined to identify conditions for Turing instability, leading to spatial pattern formation. Numerical simulations validate theoretical results, illustrating complex spatiotemporal dynamics such as oscillatory regimes and stationary patterns. Our findings highlight how Allee effects and diffusion-driven instability can shape predator–prey interactions, offering insights into ecological persistence and extinction scenarios.</p>

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Dynamics of a Leslie–Gower predator–prey model with Allee effect in predator: stability, bifurcations, and pattern formation

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Syed Adeel Gilani,
  • Qamar Din

摘要

This study investigates a modified Leslie–Gower predator–prey model incorporating an Allee effect in the predator population. We establish the existence and local stability of biologically feasible equilibria, prove the positivity and boundedness of solutions, and analyze bifurcation dynamics, including Hopf and Bogdanov–Takens (codimension-two) bifurcations around the positive equilibrium. The diffusive version of the model is further examined to identify conditions for Turing instability, leading to spatial pattern formation. Numerical simulations validate theoretical results, illustrating complex spatiotemporal dynamics such as oscillatory regimes and stationary patterns. Our findings highlight how Allee effects and diffusion-driven instability can shape predator–prey interactions, offering insights into ecological persistence and extinction scenarios.