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<p>This paper presents two predator–prey models that incorporate density-dependent predator behavior, assuming cooperation during hunting when prey is abundant and competition as prey density declines. The models are formulated as Filippov-type Leslie–Gower systems with a critical prey threshold separating behavioral regimes. The analysis focuses on the existence and stability of equilibria and pseudo-equilibria, as well as the emergence of periodic orbits. When predator cooperation occurs at high prey densities, the system exhibits sliding dynamics and may admit multiple interior equilibria together with a stable pseudo-equilibrium, possibly surrounded by a stable or unstable limit cycle. In the absence of cooperation, sliding motion disappears and a non-regular tangent point becomes dynamically relevant, potentially attracting trajectories or generating periodic oscillations. These results reveal new bifurcation phenomena in planar Filippov systems associated with the appearance or disappearance of limit cycles surrounding stable pseudo-equilibria or non-regular tangency points as a consequence of parameter perturbations, which in turn lead to local or global stability of the pseudo-equilibrium or of the non-regular tangency point.</p>

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Effect of hunting cooperation among predators in a Filippov-Leslie–Gower model with predator competition under low prey densities

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  • 发表日期：

    2026年8月5日

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  • Christian Cortés-García,
  • Jasmidt Vera-Cuenca

摘要

This paper presents two predator–prey models that incorporate density-dependent predator behavior, assuming cooperation during hunting when prey is abundant and competition as prey density declines. The models are formulated as Filippov-type Leslie–Gower systems with a critical prey threshold separating behavioral regimes. The analysis focuses on the existence and stability of equilibria and pseudo-equilibria, as well as the emergence of periodic orbits. When predator cooperation occurs at high prey densities, the system exhibits sliding dynamics and may admit multiple interior equilibria together with a stable pseudo-equilibrium, possibly surrounded by a stable or unstable limit cycle. In the absence of cooperation, sliding motion disappears and a non-regular tangent point becomes dynamically relevant, potentially attracting trajectories or generating periodic oscillations. These results reveal new bifurcation phenomena in planar Filippov systems associated with the appearance or disappearance of limit cycles surrounding stable pseudo-equilibria or non-regular tangency points as a consequence of parameter perturbations, which in turn lead to local or global stability of the pseudo-equilibrium or of the non-regular tangency point.