Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators

TL;DR

This paper investigates how external perturbations propagate through networks of synchronized oscillators, revealing resonance effects and distance-dependent response behaviors, with analytical insights and extensions to chaotic systems.

Contribution

It provides a detailed analysis of perturbation propagation in oscillator networks, linking response patterns to network structure and extending findings to chaotic oscillators.

Findings

Resonant response peaks at natural oscillator frequency

Perturbation amplitude decays exponentially with distance in small-distance regime

Similar phenomena observed in networks of chaotic oscillators

Abstract

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the interaction network underlying the ensemble. The overall response of the system is resonant, exhibiting a maximum when the perturbation frequency coincides with the natural frequency of the phase oscillators. The individual response, on the other hand, can strongly depend on the distance to the place where the perturbation is applied. For small distances on a random network, the system behaves as a linear dissipative medium: the perturbation propagates at constant speed, while its amplitude decreases exponentially with the distance. For larger distances, the response saturates to an almost constant level. These different regimes can be analytically explained in terms of the length distribution of the paths that propagate the perturbation signal. We study the extension of these results to other interaction patterns, and show that essentially the same phenomena are observed in networks of chaotic oscillators.