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<p>This paper explores a discrete-time one-prey two-predators system with Holling-III type functional responses, as well as inter-specific and intra-specific competition among predators. Firstly, we discuss the conditions for existence and local stability with respect to the equilibrium points and obtain sufficient conditions for global asymptotic stability at the interior equilibrium point by an iterative method. Secondly, we obtain sufficient conditions about the permanent coexistence of the three groups. Finally, by using explicit criterion, the bifurcation conditions for the system to occur flip bifurcation and Neimark-Sacker bifurcation at the interior equilibrium point are obtained. At the same time, numerical simulation is used to verify the analysis results.</p>

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Global Stability and Permanence of a Discrete-Time Two-Predators One-Prey System with Holling Type-III Response

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Xiongxiong Du,
  • Xiaoling Han

摘要

This paper explores a discrete-time one-prey two-predators system with Holling-III type functional responses, as well as inter-specific and intra-specific competition among predators. Firstly, we discuss the conditions for existence and local stability with respect to the equilibrium points and obtain sufficient conditions for global asymptotic stability at the interior equilibrium point by an iterative method. Secondly, we obtain sufficient conditions about the permanent coexistence of the three groups. Finally, by using explicit criterion, the bifurcation conditions for the system to occur flip bifurcation and Neimark-Sacker bifurcation at the interior equilibrium point are obtained. At the same time, numerical simulation is used to verify the analysis results.