Synchronized states in dissipatively coupled harmonic oscillator networks

TL;DR

This paper demonstrates that harmonic oscillators with slight frequency differences can synchronize through dissipative coupling, with stability achieved via gain/loss tuning, analyzed through non-Hermitian matrix eigenvalues.

Contribution

It introduces a novel synchronization mechanism for harmonic oscillators using purely dissipative coupling and stability tuning, analyzed via non-Hermitian matrix spectral properties.

Findings

Synchronization occurs despite frequency differences.

Stable dynamics achieved through gain/loss tuning.

Eigenvalue analysis explains the synchronization mechanism.

Abstract

The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely dissipative interaction. By appropriately tuned gain/loss stable dynamics may be achieved where for the cases studied in this work all oscillators are synchronized. These findings are interpreted using the complex eigenvalues and eigenvectors of the non-Hermitian matrix describing the dynamics of the system.