Chaos An Interdisciplinary Journal of Nonlinear Science

ISSN

1054-1500

1089-7682

1527-2443

Издатель

American Institute of Physics

Ключевые слова

Chaos control and syn...

Nonlinear Dynamics an...

Mathematical Dynamics...

stochastic dynamics a...

Complex Network Analy...

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Cluster dynamics in a two-group Stuart–Landau model analyzed by the second-order phase reduction
(American Institute of Physics, 2026-09-01)
Yernur Baibolatov
;
Oleh E. Omel’chenko
;
Michael Rosenblum
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.