Известия высших учебных заведений

Прикладная нелинейная динамика

ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Образец для цитирования:

Клиньшов В. В. Коллективная динамика сетей активных элементов с импульсными связями: Обзор //Известия вузов. ПНД. 2020. Т. 28, вып. 5. С. 465-490. DOI: https://doi.org/10.18500/0869-6632-2020-28-5-465-490

Опубликована онлайн: 
30.10.2020
Язык публикации: 
русский
УДК: 
530.182

Коллективная динамика сетей активных элементов с импульсными связями: Обзор

Авторы: 
Клиньшов Владимир Викторович, Нижегородский государственный университет имени Н.И.Лобачевского (ННГУ)
Тип статьи для РИНЦ: 
RAR научная статья
Аннотация: 

Цель настоящей работы – обзор исследований коллективной динамики в сетях активных элементов с импульсными связями. Для многих сетевых колебательных систем характерно межэлементное взаимодействие в форме обмена короткими сигналами, или импульсами. Важнейший класс сетевых систем, для которых характерен импульсный тип взаимодействий – биологические нейронные сети, то есть популяции нервных клеток. Описаны основные известные подходы к исследованию сетей с импульсными связями и систематизированы полученные к настоящему времени результаты. Рассматриваемые в обзоре работы используют, как правило, достаточно простые модели для описания локальной динамики элементов сети типа накопление-и-сброс или ее обобщения. Простота этих моделей позволяет во многих случаях исследовать их аналитически, и основные идеи этого анализа описаны в обзоре. Что касается структуры рассматриваемых сетей, они достаточно разнообразны и включают полносвязные сети, сети с редкими связями, многопопуляционные и модульные (кластерные) сети. Обзор структурирован по типу коллективной динамики, наблюдаемой в сетях с импульсными связями. Сначала описаны работы по синхронной динамике, исследование которой в сетях с импульсными связями было исторически первым. Далее мы переходим к асинхронной динамике, характеризующейся отсутствием корреляции между моментами генерации импульсов различными элементами сети. Важным частным случаем такой динамики является нерегулярная асинхронная динамика, рассмотренная в следующем разделе. Наконец, рассматриваются частичносинхронные режимы, характеризующиеся выраженными колебаниями среднего поля. В конце обзора систематизированы современные подходы к редукции сетевой динамики, направленные на получение низкоразмерных динамических систем, описывающих динамику сети в терминах усредненных переменных

DOI: 
10.18500/0869-6632-2020-28-5-465-490
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