Phase-locking dynamics of heterogeneous oscillator arrays

TL;DR

This paper investigates how phase-locking occurs in heterogeneous oscillator arrays with conservative coupling, analyzing stability, metastability, and the effects of nonlinear frequency dispersion through numerical simulations and phase-approximation.

Contribution

It introduces a detailed numerical study of phase-locking and its stability in heterogeneous oscillator arrays with conservative coupling, including effects of nonlinear frequency dispersion.

Findings

Global phase-locked states exist in finite lattices.

These states become unstable, leading to localized oscillations.

Metastability occurs with weak nonlinear frequency dispersion.

Abstract

We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically their destruction. Upon change of model parameters, such states are found to become unstable with the generation of localized periodic and chaotic oscillations. For weak nonlinear frequency dispersion, metastability occur akin to the case of almost-conservative systems. We also compare the results with the phase-approximation in which the amplitude dynamics is adiabatically eliminated.