Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players
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 wi...
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| Date: | 2025 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8711 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865794847099584512 |
|---|---|
| author | Karataieva, T. Koshmanenko, V. Каратаєва, Тетяна Кошманенко, Володимир |
| author_facet | Karataieva, T. Koshmanenko, V. Каратаєва, Тетяна Кошманенко, Володимир |
| author_institution_txt_mv | [
{
"author": "Тетяна Каратаєва",
"institution": "Iнститут математики НАН України, Київ"
},
{
"author": "Володимир Кошманенко",
"institution": "Інститут математики НАН України, Київ"
}
] |
| author_sort | Karataieva, T. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-09T09:33:36Z |
| description |
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. |
| doi_str_mv | 10.3842/umzh.v77i3.8711 |
| first_indexed | 2026-03-24T03:41:43Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8711 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:41:43Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-87112025-11-09T09:33:36Z Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players Характеристика рівноважних станів у моделях боротьби альтернативних опонентів при наявності зовнішньої допомоги лише окремим гравцям Karataieva, T. Koshmanenko, V. Каратаєва, Тетяна Кошманенко, Володимир dynamical system, equilibrium states, difference equations, stability динамічна система, рівноважні стани, різницеві рівняння, стійкість 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. УДК 517.9 Отримано характеристику (тип, кількість, розташування на фазовому портреті, стійкість) рівноважних станів динамічної системи, яка моделює боротьбу між індивідами абстрактного суспільства, окрема частина з яких має зовнішню допомогу. На прикладі системи з трьох індивідів детально досліджено залежність фазового портрета від значень параметра допомоги та його біфуркаційних порогів у двох випадках, коли допомога надається лише одному або лише двом гравцям. З метою можливих застосувань запропоновано інтерпретацію рівноважних станів як компромісів у конфліктній боротьбі соціальних кластерів. Institute of Mathematics, NAS of Ukraine 2025-11-07 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8711 10.3842/umzh.v77i3.8711 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 3 (2025); 163–186 Український математичний журнал; Том 77 № 3 (2025); 163–186 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8711/10433 Copyright (c) 2025 T. Karataieva, V. Koshmanenko |
| spellingShingle | Karataieva, T. Koshmanenko, V. Каратаєва, Тетяна Кошманенко, Володимир Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title | Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title_alt | Характеристика рівноважних станів у моделях боротьби альтернативних опонентів при наявності зовнішньої допомоги лише окремим гравцям |
| title_full | Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title_fullStr | Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title_full_unstemmed | Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title_short | Characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| title_sort | characteristics of equilibrium states in the models of struggle between alternative opponents in the presence of external assistance only to individual players |
| topic_facet | dynamical system equilibrium states difference equations stability динамічна система рівноважні стани різницеві рівняння стійкість |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8711 |
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