<p>This study investigates a modified Leslie-Gower predator–prey model incorporating the fear effect, the Allee effect, and spatial diffusion. Mathematical analysis establishes the positivity and boundedness of the solutions of the system, derives explicit conditions for the local and global stability of the equilibria, and identifies Hopf bifurcation conditions. For the spatial model, Turing instability is shown to drive the emergence of heterogeneous spatiotemporal patterns. Numerical simulations reveal that moderate fear has a stabilizing effect on the prey population, while excessive fear leads to its suppression. Furthermore, the Allee effect is found to significantly influence predator–prey interactions. Diffusion gives rise to cold-spotted and stripe-like spatial structures, highlighting the combined impact of behavioral, demographic, and spatial factors on species distribution and ecological stability.</p>

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Dynamics of a modified Leslie-Gower model with diffusion, fear and Allee effect

  • Hadjer Zerimeche,
  • Tarek Houmor

摘要

This study investigates a modified Leslie-Gower predator–prey model incorporating the fear effect, the Allee effect, and spatial diffusion. Mathematical analysis establishes the positivity and boundedness of the solutions of the system, derives explicit conditions for the local and global stability of the equilibria, and identifies Hopf bifurcation conditions. For the spatial model, Turing instability is shown to drive the emergence of heterogeneous spatiotemporal patterns. Numerical simulations reveal that moderate fear has a stabilizing effect on the prey population, while excessive fear leads to its suppression. Furthermore, the Allee effect is found to significantly influence predator–prey interactions. Diffusion gives rise to cold-spotted and stripe-like spatial structures, highlighting the combined impact of behavioral, demographic, and spatial factors on species distribution and ecological stability.