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<p>Qualitative analysis of a Leslie-Gower predator-prey model with weak Allee effect and refuge in the prey is explored and some theoretical results further are validated by numerical simulation of MATLAB in this paper. Through the analysis of the dynamic behavior of the origin by blow-up method, once the intensity of predation and the Allee effect of the prey are too large, the establishment of refuge is conducive to the coexistence of predators and populations. In addition, by means of Dulac-Bendixson theorem, the sufficient conditions for global asymptotic stability of the positive equilibrium are found. Furthermore, sufficient conditions of the number and stability of limit cycles are determined with parameters in large range. Finally, it is concluded that Hopf bifurcation can only produce a stable limit cycle under disturbance.</p>

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Qualitative analysis of a Leslie-Gower model with proportional refuge and weak Allee effect in prey

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • Zhenliang Zhu,
  • Shangming Chen,
  • Linyuan Fan,
  • Geng Lin

摘要

Qualitative analysis of a Leslie-Gower predator-prey model with weak Allee effect and refuge in the prey is explored and some theoretical results further are validated by numerical simulation of MATLAB in this paper. Through the analysis of the dynamic behavior of the origin by blow-up method, once the intensity of predation and the Allee effect of the prey are too large, the establishment of refuge is conducive to the coexistence of predators and populations. In addition, by means of Dulac-Bendixson theorem, the sufficient conditions for global asymptotic stability of the positive equilibrium are found. Furthermore, sufficient conditions of the number and stability of limit cycles are determined with parameters in large range. Finally, it is concluded that Hopf bifurcation can only produce a stable limit cycle under disturbance.