Nonlinearly coupled harmonic oscillators: high frequency oscillations yield synchronization

TL;DR

This paper studies how nonlinear coupling in harmonic oscillators leads to synchronization, demonstrating that under certain conditions, the oscillators' frequencies become aligned despite complex interactions.

Contribution

It introduces a novel analysis of synchronization in nonlinear, unidirectional coupled oscillators with a specific coupling function, proving stability of the synchronized state.

Findings

Synchronization manifold is semiglobally practically asymptotically stable.

High frequency oscillations facilitate synchronization.

Connectivity of the network is essential for stability.

Abstract

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the relative distance (between the states of the pair being coupled) vector. Under the assumption that the interconnection topology defines a connected graph, it is shown that the synchronization manifold is semiglobally practically asymptotically stable in the frequency of oscillations.