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

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.

Revised version published in AIP Advances 13, 035222 (2023)

References in corpus (2)

• (Vanishing) Twist in the Saddle-Centre and Period-Doubling Bifurcation
• Computational capabilities at the edge of chaos for one dimensional system undergoing continuous transitions

Cited by in corpus (1)

• Non-linear oscillators with Kuramoto-like local coupling: Complexity analysis and spatiotemporal pattern generation