dongu-vestnik04.ru Вестник Донецкого университета. Серия 04. Технические науки Vestnik of Donetsk University. Series 04. Technical Sciences 2663-4228 513 10.5281/zenodo.19201881 Articles Статьи Research Article PHENOMENOLOGICAL APPROACH TO THE COMPLEX ASSESSMENT OF THE COMPLEXITY OF MULTIDIMENSIONAL SYSTEMS ФЕНОМЕНОЛОГИЧЕСКИЙ ПОДХОД К КОМПЛЕКСНОЙ ОЦЕНКЕ СЛОЖНОСТИ МНОГОМЕРНЫХ СИСТЕМ https://orcid.org/0000-0003-1070-3677 Averin Gennadii Viktorovich Аверин Геннадий Викторович averin.gennadiy@gmail.com 1 https://orcid.org/0000-0003-2218-9230 Zviagintseva Anna Viktorovna Звягинцева Анна Викторовна a.zvyagintseva@donnu.ru 2 https://orcid.org/0009-0005-4420-9206 Brazhnikov Andrei Romanovich Бражников Андрей Романович yanox123321@gmail.com 3 ФГБОУ ВО «Донецкий государственный университет» Donetsk State University ФГБОУ ВО «Донецкий государственный университет» Donetsk State University ФГБОУ ВО «Донецкий государственный университет» Donetsk State University 1 NO1 (27.0) №1 (27.0) 124 140 15 07 2026 Copyright ©; 2026, Вестник Донецкого университета. Серия 04. Технические науки Copyright ©; 2026, Vestnik of Donetsk University. Series 04. Technical Sciences 2026 Вестник Донецкого университета. Серия 04. Технические науки Vestnik of Donetsk University. Series 04. Technical Sciences Эта статья распространяется на условиях лицензии Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0) https://dongu-vestnik04.ru/index.php/vestnik04/article/view/513

The article discusses the problem of quantifying the complexity of multidimensional non-stationary systems, which is relevant for areas such as monitoring financial markets, climate processes, and technical systems. It analyzes existing approaches, including entropy-based, algorithmic, early warning signal (EWS), and structural methods. The article identifies limitations of these methods in terms of their universality and complexity. The proposed approach focuses on phenomenological modeling and identifying stable macroscopic patterns of complexity by applying general system models for analyzing and interpreting empirical data. Developed phenomenological models of describing the state space of the system based on data and proposed various integral measures of complexity. Formulated criteria for assessing the structural, dynamic, systemic, descriptive and relative complexity of systems. The phenomenological approach allows for universal application to multidimensional systems of various natures.

В статье рассматривается проблема количественной оценки сложности многомерных нестационарных систем, актуальная для таких областей, как мониторинг финансовых рынков, климатических процессов и технических систем. Проведен анализ существующих подходов – энтропийного, алгоритмического, методов ранних предупреждающих сигналов (EWS) и структурных методов. Выявлены ограничения данных методов в части универсальности и комплексности. Идея предлагаемого подхода направлена на феноменологическое моделирование и выявление устойчивых макроскопических закономерностей сложности на основе применения общесистемных моделей анализа и интерпретации эмпирических данных. Разработаны феноменологические модели описания пространства состояний системы на основе данных и предложены различные интегральные меры сложности. Сформулированы критерии оценки структурной, динамической, системной, описательной и относительной сложности систем. Феноменологический подход позволяет обеспечивать универсальность применения по отношению к многомерным системам различной природы.

 complexity, multidimensional systems, phenomenological models, information measures, complexity criteria, comprehensive assessment сложность, многомерные системы, феноменологические модели, информационные меры, критерии сложности, комплексная оценка

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