Behaviour of circular chains of nonlinear oscillators with Kuramoto-like local coupling

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units. Instead of global couplings, nearest-neighbor interaction is as...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: K García Medina, Estevez-Rams, E
Format: Article
Language:English
Subjects:
Couplings
Order parameters
Oscillators
Resonant frequencies
Synchronism
Online Access:Get full text
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Summary:The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units. Instead of global couplings, nearest-neighbor interaction is assumed. Units are pairwise coupled by a Kuramoto term driven by their phase differences. The system exhibits a rich set of behaviors depending on the balance between the natural frequency of isolated units and the self-feedback. The case of two oscillators is solved analytically, while a numerical approach is used for \(N>2\). Building from Kuramoto, the approach to synchronization, when possible, is studied through a local complex order parameter. The system can eventually evolve as a set of coupled local communities towards a given phase value. However, the approach to the stationary state shows a non-monotonous non-trivial dynamic.
ISSN:2331-8422
DOI:10.48550/arxiv.2310.12165