Heterogeneity induces emergent functional networks for synchronization

TL;DR

This paper investigates how heterogeneity in oscillator networks leads to the emergence of functional networks with hubs, influencing synchronization and control strategies.

Contribution

It reveals that node heterogeneity shapes the architecture of functional networks and introduces a local evolutionary strategy for synchronization control.

Findings

Heterogeneity causes differentiation in link activation probabilities.

Hubs form around nodes with larger frequency deviations.

The approach can be applied to various synchronization problems.

Abstract

We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We demonstrate that increasing heterogeneity among the nodes in state-dependent networks of phase oscillators causes a differentiation in the activation probabilities of the links. This, in turn, yields the formation of hubs associated to nodes with larger distances from the average frequency of the ensemble. Our generic local evolutionary strategy can be used to solve a wide range of synchronization and control problems.