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arXiv · 2310.12165

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

K. García Medina·E. Estevez-Rams
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Abstract

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.

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K. García Medina, E. Estevez-Rams. 2023-10-01. Behaviour of circular chains of nonlinear oscillators with Kuramoto-like local coupling. https://doi.org/10.1063/5.0135667

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