Propagation of small perturbations in synchronized oscillator networks

TL;DR

This paper investigates how small harmonic perturbations propagate through synchronized oscillator networks, revealing a distance-dependent exponential decay and constant propagation speed, with implications for understanding interaction patterns.

Contribution

It provides an analytical and numerical analysis of perturbation propagation in synchronized oscillator networks, highlighting a linear dissipative behavior and potential for network structure inference.

Findings

Perturbations decay exponentially with distance from the source.

Propagation occurs at a constant speed across the network.

Response patterns can help deduce network interactions.

Abstract

We study the propagation of a harmonic perturbation of small amplitude on a network of coupled identical phase oscillators prepared in a state of full synchronization. The perturbation is externally applied to a single oscillator, and is transmitted to the other oscillators through coupling. Numerical results and an approximate analytical treatment, valid for random and ordered networks, show that the response of each oscillator is a rather well-defined function of its distance from the oscillator where the external perturbation is applied. For small distances, the system behaves as a dissipative linear medium: the perturbation amplitude decreases exponentially with the distance, while propagating at constant speed. We suggest that the pattern of interactions may be deduced from measurements of the response of individual oscillators to perturbations applied at different nodes of the network.