Behavior 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, the nearest-neighbor interaction i...

Full description

Saved in:
Bibliographic Details
Published in:AIP advances 2023-03, Vol.13 (3), p.035222-035222-8
Main Authors: Medina, K. García, Estevez-Rams, E.
Format: Article
Language:English
Subjects:
Couplings
Order parameters
Oscillators
Resonant frequencies
Synchronism
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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, the 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 toward a given phase value. However, the approach to the stationary state shows a non-monotonous non-trivial dynamic.
ISSN:2158-3226
2158-3226
DOI:10.1063/5.0135667