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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">vmait</journal-id><journal-title-group><journal-title xml:lang="ru">Computational Mathematics and Information Technologies</journal-title><trans-title-group xml:lang="en"><trans-title>Computational Mathematics and Information Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2587-8999</issn><publisher><publisher-name>Донской государственный технический университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.23947/2587-8999-2020-1-2-87-93</article-id><article-id custom-type="elpub" pub-id-type="custom">vmait-19</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Моделирование системы «власть-общество» с двумя бюрократическими кланами и биполярной реакцией общества</article-title><trans-title-group xml:lang="en"><trans-title>Modeling the «power-society» system with two bureaucratic clans and bipolar reaction of the society</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михайлов</surname><given-names>А. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhailov</surname><given-names>A. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михайлов Александр Петрович, доктор физико-математических наук, главный научный сотрудник</p><p>Москва, Миусская пл., 4</p></bio><bio xml:lang="en"><p>Mikhailov Alexander P., Dr.Sci. (Math), Chief Researcher</p><p>4, Miusskaya Sq., Moscow</p></bio><email xlink:type="simple">apmikhailov@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Прончев</surname><given-names>Г. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Pronchev</surname><given-names>G. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Прончев Геннадий Борисович, кандидат физико-математических наук, зам. заведующего кафедрой, доцент, Социологический факультет</p><p>Москва, Ленинские горы, 1, стр. 33</p></bio><bio xml:lang="en"><p>Pronchev Gennadiy B., Ph.D., Associate Professor at Department of Sociological Research Methodology</p><p>Leninskiye Gory, 1, Building 33, Moscow</p></bio><email xlink:type="simple">pronchev@rambler.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт прикладной математики им. М.В. Келдыша РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Keldysh Institute of Applied Mathematics RAS</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>МГУ им. М.В. Ломоносова</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Lomonosov Moscow State University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>20</day><month>02</month><year>2023</year></pub-date><volume>4</volume><issue>2</issue><fpage>87</fpage><lpage>93</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Михайлов А.П., Прончев Г.Б., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Михайлов А.П., Прончев Г.Б.</copyright-holder><copyright-holder xml:lang="en">Mikhailov A.P., Pronchev G.B.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.cmit-journal.ru/jour/article/view/19">https://www.cmit-journal.ru/jour/article/view/19</self-uri><abstract><p>В статье исследуется модель системы «Власть-Общество» с двумя кланами и биполярной реакцией общества. Модель «Власть-Общество» описывает динамику распределения власти в иерархии с учетом влияния общества. Модель «Власть-Общество» с непрерывным временем имеет форму параболического уравнения в случае непрерывной иерархии и форму системы обыкновенных дифференциальных уравнений в случае дискретной иерархии. Рассматриваемая в данной статье модель с дискретным временем представляет собой систему пять динамических уравнений. Биполярная реакция общества описывает ситуацию с двумя устойчивыми распределениями власти; другими словами, для каждого государственного чиновника возможны два значения объема власти, каждое из которых рассматривается обществом как желательное. Если каждый чиновник реализует больший объем власти из этих двух, то имеет место распределение «сильной руки», если все они реализуют меньший объем, то имеет место партиципаторное распределение. Под бюрократическим кланом понимается объединение бюрократов, имеющих общий интерес и преследующих общие цели, вообще говоря, отличные от целей общества в целом. В статье рассматривается иерархия из пяти должностных лиц, из которых один является первоиерархом, а четыре других образуют два конкурирующих клана. Система изучается численно. Показано, в частности, что в этой системе властолюбие клана существенно влияет на то, насколько быстро ему удается увеличить свою власть, однако само достигнутое количество власти почти не зависит от властолюбия, а определяется реакция общества.</p></abstract><trans-abstract xml:lang="en"><p>The paper studies the model of «Power-Society» system with two clans and bipolar reaction of the society. The «Power-Society» model describes the dynamics of distribution of power in hierarchy. This dynamics is influenced by society. Continuous-time «Power-Society» model has the form of parabolic equation in the case of continuous hierarchy, and the form of system of ordinary differential equations in the case of discrete hierarchy. The discrete-time model considered in this paper has the form of five dynamical equations. Bipolar reaction of the society refers to the situation with two stable distributions of power. In other words, for each government official two values are possible for the volume of power. Each of these values is considered by society as desirable. If each official holds the greater volume, we say that there is the «strong hand» distribution, if they all hold the smaller volume, this is the participatory distribution. Bureaucratic clans are an association of bureaucrats united by common interests and pursuing common goals, generally speaking, different from those of society as a whole. The paper considers a simple hierarchy of five officials, of which one is the head and four others form two competing clans. The system is studied numerically. It is shown, in particular, that in this system, the clan's lust for power significantly affects how quickly it manages to increase its power, however, the achieved amount of power itself almost does not depend on the lust for power, but is determined by the reaction of society.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическое моделирование</kwd><kwd>динамическая модель</kwd><kwd>система «Власть-Общество»</kwd><kwd>политические кланы</kwd><kwd>численный эксперимент</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical modeling</kwd><kwd>dynamic model</kwd><kwd>«Power–Society» system</kwd><kwd>political clans</kwd><kwd>numerical experiment</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено при финансовой поддержке РФФИ в рамках научного проекта № 19-01-00089-a</funding-statement><funding-statement xml:lang="en">The reported study was supported by Russian Foundation for Basic Research (project 19-01-00089-a)</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Collins K. 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