Collective stochastic coherence and synchronizability in weighted scale-free networks

TL;DR

This paper demonstrates that weighted scale-free networks of coupled excitable elements can simultaneously achieve high synchronizability and strong collective noise response, overcoming a fundamental apparent conflict.

Contribution

It introduces a coupling architecture in weighted scale-free networks that reconciles synchronization and noise response, a novel finding in network dynamics.

Findings

Weighted scale-free networks exhibit both high synchronizability and good noise response.

Link homogeneity due to weighting balances degree heterogeneity in SFNs.

Compared to unweighted and regular networks, weighted SFNs outperform in these properties.

Abstract

Coupling frequently enhances noise-induced coherence and synchronization in interacting nonlinear systems, but it does so separately. In principle collective stochastic coherence and synchronizability are incompatible phenomena, since strongly synchronized elements behave identically and thus their response to noise is indistinguishable to that of a single element. Therefore one can expect systems that synchronize well to have a poor collective response to noise. Here we show that, in spite of this apparent conflict, a certain coupling architecture is able to reconcile the two properties. Specifically, our results reveal that weighted scale-free networks of diffusively coupled excitable elements exhibit both high synchronizability of their subthreshold dynamics and a good collective response to noise of their pulsed dynamics. This is established by comparing the behavior of this system to that of random, regular, and unweighted scale-free networks. We attribute the optimal response of weighted scale-free networks to the link homogeneity (with respect to node degree) provided by the weighting procedure, which balances the degree heterogeneity typical of SFNs.