vestnikmephiВестник НИЯУ МИФИVestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI"2304-487XNational Research Nuclear University "MEPhI"10.26583/vestnik.2025.4.4MJQWILvestnikmephi-437Research ArticleМАТЕМАТИЧЕСКИЕ МОДЕЛИ И ЧИСЛЕННЫЕ МЕТОДЫMATHEMATICAL MODELS AND NUMERICAL METHODSИсследование процессов самоорганизации в бактериальных колониях, описываемых моделью Чави – Вадди – КолокольниковаInvestigation of self-organization processes in bacterial colonies described by the Chavi-Waddy-Kolokolnikov model equationГоловковА. Г.GolovkovA. G.

кафедра «Прикладная математика» (№31), инженер

gag006@campus.mephi.ruРябовП. Н.RyabovP. N.

к.ф.-м.н.

кафедра «Прикладная математика» (№31), доцент

pnryabov@mephi.ruhttps://orcid.org/0000-0001-5926-9715КудряшовН. А.KudryashovN. A.

доктор физико-математических наук, профессор

кафедра «Прикладная математика» (№31), главный научный сотрудник, заведующий кафедрой

nakudryashov@mephi.ruНациональный исследовательский ядерный университет «МИФИ»РоссияNational Research Nuclear University MEPhI (Moscow Engineering Physics Institute)Russian Federation202531082025144318331Copyright © Головков А.Г., Рябов П.Н., Кудряшов Н.А., 20252025Головков А.Г., Рябов П.Н., Кудряшов Н.А.Golovkov A.G., Ryabov P.N., Kudryashov N.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnikmephi.elpub.ru/jour/article/view/437

Исследована обобщенная модель Чави – Вадди – Колокольникова, применяемая для описания пространственно-временной динамики бактериальных колоний с учетом возможной «дисперсии» – механизма, отвечающего за миграцию и перераспределение популяции в окружающей среде. С биологической точки зрения благодаря рассматриваемой модели удается понять, как бактериальные клетки, способные к коллективному движению, формируют упорядоченные структуры (например, скопления или волны) даже при наличии внешних возмущений. Основной фокус работы направлен на исследование динамики системы бактериальных колоний, описываемых обобщенной моделью Чави – Вади – Колокольникова. Так, в работе разработан численный алгоритм для проведения математического моделирования данных процессов, проведена его верификация на базе точных решений рассматриваемой модели в виде уединенных волн. Исследовано влияние параметров задачи на поведение системы бактериальных колоний. Помимо этого, основное внимание в работе уделено изучению процессов самоорганизации бактерий, а также классификации динамики поведения системы для различных значений параметров рассматриваемой задачи.

The generalized Chavi-Waddy-Kolokolnikov model used to describe the spatial and temporal dynamics of bacterial colonies is studied, taking into account possible “dispersion” – the mechanism responsible for migration and redistribution of the population in the environment. From a biological point of view, the model allows us to understand how bacterial cells, capable of collective movement, form ordered structures (e.g., clusters or waves) even in the presence of external disturbances. The main focus of the work is on the study of the dynamics of the bacterial colony system described by the generalized Chavi-Wadi-Kolokolnikov model. Thus, a numerical algorithm for mathematical modeling of these processes has been developed and its verification has been carried out on the basis of exact solutions of the model in the form of solitary waves. The influence of the problem parameters on the behavior of the bacterial colony system was investigated. In addition, the main attention in the work is paid to the study of bacterial self-organization processes, as well as to the classification of the dynamics of the system behavior for different values of the parameters of the problem under consideration.

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The authors declare that there are no conflicts of interest present.