Connectivity-Driven Coherence in Complex Networks

TL;DR

This paper investigates how the coherence in complex networks depends on connectivity, dynamics, and coupling, revealing how network structure influences emergent synchronized behavior and how to control it.

Contribution

It provides a detailed analysis of the relationship between network connectivity and coherence, including effects of random and local connections, and offers methods to control emergent coherence.

Findings

Coherence scales with mean degree in random graphs.

In locally connected networks, coherence depends on how mean degree scales with size.

Adding random connections enhances coherence proportionally to the fraction added.

Abstract

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the coupling function. These findings predict that in random graphs, the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree, but rather on how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.