Pattern phase diagram for 2D arrays of coupled limit-cycle oscillators

TL;DR

This paper develops a phase diagram for 2D arrays of coupled limit-cycle oscillators, revealing complex patterns and dynamics beyond traditional models, with implications for nano- and optomechanical systems.

Contribution

It introduces a comprehensive phase diagram for phase dynamics in 2D oscillator arrays, extending beyond Kuramoto models, and discusses experimental relevance.

Findings

Identification of stationary and non-stationary patterns

Analysis of phase evolution in 2D arrays

Potential observation in optomechanical systems

Abstract

Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. They are also of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays. We find that the full dynamical equations for the phase dynamics of such an array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and non-stationary patterns. The possible observation in optomechanical arrays is discussed briefly.