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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 custom-type="elpub" pub-id-type="custom">vmait-82</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 влияния политической поляризации на исход пропагандистского противоборства</article-title><trans-title-group xml:lang="en"><trans-title>Modeling the Effect of Political Polarization on the Outcome of Propaganda Battle</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>Александр Петрович</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhailov</surname><given-names>Alexander P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михайлов Александр Петрович, доктор физико-математических наук, профессор заведующий сектором Института прикладной математики им. М.В.Келдыша РАН (РФ, г. Москва, Миусская пл.,4)</p></bio><bio xml:lang="en"><p>Mikhailov Alexander P., Dr.Sci. (Math), professor, head of the Group Keldysh Institute of Applied Mathematics (4, Miusskaya Sq., Moscow, Russian Federation)</p></bio><email xlink:type="simple">apmikhailov@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5244-8286</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Петров</surname><given-names>Александр Пхоун Чжо</given-names></name><name name-style="western" xml:lang="en"><surname>Petrov</surname><given-names>Alexander P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Петров Александр Пхоун Чжо, доктор физико-математических наук, ведущий научный сотрудник Института прикладной математики им. М.В.Келдыша РАН (РФ, г. Москва, Миусская пл.,4)</p></bio><bio xml:lang="en"><p>Petrov Alexander P., Dr.Sci. (Math), Leading Researcher Keldysh Institute of Applied Mathematics (4, Miusskaya Sq., Moscow, Russian Federation)</p></bio><email xlink:type="simple">petrov.alexander.p@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>Прончева</surname><given-names>Ольга Геннадьевна</given-names></name><name name-style="western" xml:lang="en"><surname>Proncheva</surname><given-names>Olga G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Прончева Ольга Геннадьевна, аспирант Института прикладной математики им. М.В.Келдыша РАН (РФ, г. Москва, Миусская пл.,4)</p></bio><bio xml:lang="en"><p>Proncheva Olga G., Postgraduate Student Keldysh Institute of Applied Mathematics (4, Miusskaya Sq., Moscow, Russian Federation)</p></bio><email xlink:type="simple">olga.proncheva@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт прикладной математики им. М.В.Келдыша РАН&#13;
(РФ, г. Москва, Миусская пл.,4)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Keldysh Institute of Applied Mathematics &#13;
(4, Miusskaya Sq., Moscow, Russian Federation)</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2017</year></pub-date><pub-date pub-type="epub"><day>29</day><month>03</month><year>2023</year></pub-date><volume>1</volume><issue>1</issue><elocation-id>82</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Михайлов А.П., Петров А.П., Прончева О.Г., 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder xml:lang="ru">Михайлов А.П., Петров А.П., Прончева О.Г.</copyright-holder><copyright-holder xml:lang="en">Mikhailov A.P., Petrov A.P., Proncheva O.G.</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/82">https://www.cmit-journal.ru/jour/article/view/82</self-uri><abstract><p>Комплекс вопросов, связанных с пропагандистским противоборством и, более широко, с влиянием целенаправленно распространяемой информации на общество, привлекает неослабевающее внимание исследователей различных специальностей – социологов, специалистов в области информационных технологий и математиков. Модель выбора позиций индивидами при пропагандистском противоборстве применяется к изучению вопроса о влиянии степени поляризации общества на исход противостояния. Для этого рассмотрен случай распределения индивидов, соответствующего обществу, состоящему из двух групп, придерживающихся противоположных установок по некоторому вопросу. В настоящей работе развивается подход, акцентированный на модели информационного противоборства – именно, на выборе позиций индивидами при противоборстве. В основе этой модели лежит нейрологическая схема Рашевского.Данная модель прилагается к изучению вопроса о том, как уровень политической поляризации влияет на исход пропагандистской борьбы. Данная постановка вопроса становится возрастающее актуальной, в первую очередь, в связи с развитием социальных медиа. В последнее время в литературе широко обсуждается вопрос об усилении поляризации в связи с развитием социальных медиа и вообще Интернета, а также о влиянии поляризации на политические события. В настоящей работе поляризованное общество описывается с помощью кривой распределения, имеющей два высоких горизонтальных плато. Расстояние между центрами тяжести этих плато принимается за меру поляризации. Таким образом, процесс возрастания поляризации имеет вид взаимного удаления плато друг от друга. Модель исследована аналитически и численно. Показано, что умеренная политическая поляризация благоприятствует стороне, имеющей превосходство в интенсивности пропаганды. Однако, если поляризация слишком сильна, то она нивелирует преимущество в пропаганде.</p></abstract><trans-abstract xml:lang="en"><p>The paper adds to the literature on propaganda wars. This area attracts practitioners as well as researchers from a variety of fields such as philosophy, social and political science, psychology. It also attracts IT researchers and mathematicians who develop and study models of propaganda wars. In this paper we apply the mathematical model of making choices by individuals to the problem of how the extent of social polarization affects the outcome of the propaganda battle. By the term “propaganda battle” we mean that each member of the society is subject to two competing flows of information. These two flows are generated by two competing parties and each flow consists of propaganda and rumor. That is each party runs propaganda via its own mass-media, and the rumor adds to propaganda as individuals get information from media and transmit it further through interpersonal communications with other individuals. The kind of society is considered which comprises two groups with diametrically opposite fundamental attitudes. The mathematical model has been investigated analytically and numerically. It is shown that moderate political polarization favors the side that runs more intensive propaganda. However, the advantage of stronger propaganda is impaired if the polarization is great enough, because neither media nor individuals can reassure their radical opponents.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>математическое моделирование</kwd><kwd>пропагандистское противоборство</kwd><kwd>нейрологическая схема Рашевского</kwd><kwd>конкурирующие информационные потоки</kwd></kwd-group><kwd-group xml:lang="en"><kwd>mathematical modeling</kwd><kwd>propaganda battle</kwd><kwd>Rashevsky’s neurological scheme</kwd><kwd>competing rumors</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Работа выполнена при поддержке Российского фонда фундаментальных исследований, проекты 16-01-0100306, 17-01-01390</funding-statement><funding-statement xml:lang="en">This research was supported by Russian foundation for Basic Research (projects 16-01-0100306, 17-01-01390)</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">Chomsky N. 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