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<p>We determine the characteristics (type, number, position in the phase portrait, and stability) of the equilibrium states of a dynamical system simulating the competition of individuals in an abstract society some part of which receives external assistance. By analyzing a system with three individuals as an example, we propose the detailed description of dependence of the phase portrait of the system on the values of the parameter of assistance and its bifurcation thresholds for two cases where the assistance is provided only to one or to two players. For possible applications, we propose the interpretation of equilibrium states as compromises in the conflict competition of social clusters.</p>

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Characteristics of Equilibrium States in the Models of Competition Between Alternative Opponents in the Presence of External Assistance Only to Individual Players

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Tetiana Karataieva,
  • Volodymyr Koshmanenko

摘要

We determine the characteristics (type, number, position in the phase portrait, and stability) of the equilibrium states of a dynamical system simulating the competition of individuals in an abstract society some part of which receives external assistance. By analyzing a system with three individuals as an example, we propose the detailed description of dependence of the phase portrait of the system on the values of the parameter of assistance and its bifurcation thresholds for two cases where the assistance is provided only to one or to two players. For possible applications, we propose the interpretation of equilibrium states as compromises in the conflict competition of social clusters.