Cluster dynamics in a two-group Stuart–Landau model analyzed by the second-order phase reduction

Yernur Baibolatov; Oleh E. Omel’chenko; Michael Rosenblum

doi:10.1063/5.0346282

Cluster dynamics in a two-group Stuart–Landau model analyzed by the second-order phase reduction

Автор(ы)

Yernur Baibolatov

Oleh E. Omel’chenko

Michael Rosenblum

Дата публикации

1 сентября 2026 г.

Тип

journal article

Издатель

American Institute of Physics

Журнал

Chaos An Interdisciplinary Journal of Nonlinear Science

Том

36

Выпуск

9

DOI

10.1063/5.0346282

ISSN

1054-1500

Аннотация

We analyze cluster states in an ensemble of Stuart-Landau oscillators with two subpopulations of different frequencies. Our main goal is to compare the descriptions of the system's dynamics obtained via the standard first-order phase approximation and the second-order phase reduction. We demonstrate that the second-order model not only provides quantitative improvements in the description but also reveals new dynamical states not present in the standard Kuramoto theory. In particular, it describes bistability of synchronous states in the minimal setup of two coupled oscillators and the existence of three-cluster states, forbidden in the first-order phase description by the Watanabe-Strogatz theory. The very good agreement between the second-order approximation results and the results of numerical simulations of the original Stuart-Landau network highlights the usefulness of high-order phase-reduction models.

Темы

Stuart-Landau oscilla...

cluster states

coupled oscillators

Области науки (FoS)

Computer Science

Computer Networks and...

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Название

W7163538918.pdf

Описание

Полный текст в открытом доступе, лицензия cc-by; источник: https://arxiv.org/pdf/2606.04668

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1,27 MB

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