Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players

Authors

  • T. Karataieva Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv
  • V. Koshmanenko Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv

DOI:

https://doi.org/10.3842/umzh.v77i3.8711

Keywords:

dynamical system, equilibrium states, difference equations, stability

Abstract

UDC 517.9

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

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Published

07.11.2025

Issue

Vol. 77 No. 3 (2025)

Section

Research articles

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Copyright (c) 2025 T. Karataieva, V. Koshmanenko

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How to Cite

Karataieva, T., and V. Koshmanenko. “Characteristics of Equilibrium States in the Models of Struggle Between Alternative Opponents in the Presence of External Assistance Only to Individual Players”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 3, Nov. 2025, pp. 163–186, https://doi.org/10.3842/umzh.v77i3.8711.