Experimental implementation of maximally synchronizable networks

TL;DR

This paper demonstrates experimentally how to transform coupled oscillator networks into maximally synchronizable acyclic networks by tuning weights, enhancing synchronization stability and robustness against topological uncertainties.

Contribution

It introduces a practical method to convert networks into MSNs, optimizing synchronizability and analyzing robustness through experimental electronic oscillator networks.

Findings

Tuning network weights achieves minimal eigenratio for maximal synchronizability.

Experimental validation confirms robustness of MSNs against topological uncertainties.

Propagation of synchronization errors is effectively studied in physical oscillator networks.

Abstract

Maximally synchronizable networks (MSNs) are acyclic directed networks that maximize synchronizability. In this paper, we investigate the feasibility of transforming networks of coupled oscillators into their corresponding MSNs. By tuning the weights of any given network so as to reach the lowest possible eigenratio $\lambda_N/\lambda_2$, the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths. We check the robustness of the resulting MSNs with an experimental implementation of a network of nonlinear electronic oscillators and study the propagation of the synchronization errors through the network. Importantly, a method to study the effects of topological uncertainties on the synchronizability is proposed and explored both theoretically and experimentally.