Stable resonances and signal propagation in a chaotic network of coupled units

TL;DR

This paper investigates how weak periodic signals propagate through a chaotic network of nonlinear units using linear response theory, revealing stable resonances that depend on specific unit pairs and influence signal transmission.

Contribution

It introduces the concept of stable resonances in chaotic networks and demonstrates their dependence on unit pairs, advancing understanding of signal propagation in nonlinear systems.

Findings

Identification of stable resonances in chaotic networks

Resonances depend on specific unit pairs

Units exhibit different signal transmission capabilities

Abstract

We apply the linear response theory developed in \cite{Ruelle} to analyze how a periodic signal of weak amplitude, superimposed upon a chaotic background, is transmitted in a network of non linearly interacting units. We numerically compute the complex susceptibility and show the existence of specific poles (stable resonances) corresponding to the response to perturbations transverse to the attractor. Contrary to the poles of correlation functions they depend on the pair emitting/receiving units. This dynamic differentiation, induced by non linearities, exhibits the different ability that units have to transmit a signal in this network.