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Equilibrium States of the Dynamic Conflict System for Three Players with a Parameter of Influence of the Ambient Environment

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We study the mathematical model of an abstract society in the form of a complex dynamical system with conflict interaction between its elements. New existence conditions are established for equilibrium (compromise) states (fixed points) in the presence of a permanent influence of the environment. Our main results are obtained for systems with three elements (players). In this case, we give a description of all equilibrium states, study their stability depending on the parameter of external influence, and partially describe the basins of attraction for one-point attractors. Several numerical examples are presented.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka Str., 3, Kyiv, 01024, Ukraine

    T. V. Karataieva & V. D. Koshmanenko

  2. National Pedagogical Dragomanov University, Pirogova St., 9, Kyiv, 01601, Ukraine

    V. D. Koshmanenko

Authors
  1. T. V. Karataieva
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  2. V. D. Koshmanenko
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Correspondence to V. D. Koshmanenko.

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Translated from Neliniini Kolyvannya, Vol. 25, No. 2-3, pp. 207–225, April–September, 2022.

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Karataieva, T.V., Koshmanenko, V.D. Equilibrium States of the Dynamic Conflict System for Three Players with a Parameter of Influence of the Ambient Environment. J Math Sci 274, 861–880 (2023). https://doi.org/10.1007/s10958-023-06649-x

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  • DOI: https://doi.org/10.1007/s10958-023-06649-x

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