Synchronization of fluctuating delay-coupled chaotic networks

TL;DR

This paper investigates how fluctuating time-delayed interactions in chaotic networks can enhance synchronization, revealing that fast fluctuations improve stability while slow ones diminish it, with resonance effects at intermediate scales.

Contribution

It demonstrates that rapid fluctuations in network connections can significantly enhance synchronization stability in delay-coupled chaotic networks, a novel insight into dynamic network behavior.

Findings

Fast fluctuations increase synchronizability.

Slow fluctuations diminish synchronization.

Resonance effects occur at intermediate fluctuation timescales.

Abstract

We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties of static and fluctuating networks, we find that random network alternations can enhance the synchronizability. Synchronized states appear to be maximally stable when fluctuations are much faster than the time-delay, even when the instantaneous state of the network does not allow synchronization. This enhancing effect disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, a desynchronizing resonance is reported. Moreover, we observe characteristic oscillations, with a periodicity related to the coupling delay, as the system approaches or drifts away from the synchronized state.