Optimal phase synchronization in networks of phase-coherent chaotic oscillators

TL;DR

This paper explores how the natural frequencies and network topology influence phase synchronization in chaotic oscillators, proposing a synchrony alignment function that optimizes coupling strength and demonstrating its effectiveness through numerical, experimental, and electronic circuit tests.

Contribution

It introduces a synchrony alignment function linking natural frequencies and network topology for phase-coherent chaotic oscillators, extending previous models and validating with experiments.

Findings

Optimal interplay reduces coupling strength for synchronization

Synchrony alignment function effectively predicts synchronization conditions

Experimental results confirm robustness despite noise and parameter mismatch

Abstract

We investigate the existence of an optimal interplay between the natural frequencies of a group chaotic oscillators and the topological properties of the network they are embedded in. We identify the conditions for achieving phase synchronization in the most effective way, i.e., with the lowest possible coupling strength. Specifically, we show by means of numerical and experimental results that it is possible to define a synchrony alignment function linking the natural frequencies of a set of non-identical phase-coherent chaotic oscillators with the topology of the Laplacian matrix $L$, the latter accounting for the specific organization of the network of interactions between oscillators. We use the classical R\"ossler system to show that the synchrony alignment function obtained for phase oscillators can be extended to phase-coherent chaotic systems. Finally, we carry out a series of experiments with nonlinear electronic circuits to show the robustness of the theoretical predictions despite the intrinsic noise and parameter mismatch of the electronic components.