Optimal synchronization on strongly connected directed networks

TL;DR

This paper designs and analyzes strongly connected sparse directed networks with enhanced synchronization properties, focusing on spectral characteristics and network organization to optimize synchronization performance.

Contribution

It introduces two types of PFS-enhanced networks and relates their synchronization properties to network structure and spectral features.

Findings

Eigenratio minimizing networks have complex spectra with non-vanishing imaginary parts.

Networks with real spectra have slightly larger eigenratios but different structural features.

Enhanced synchronization is linked to skewed out-degree distribution and hierarchical organization.

Abstract

In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the particular organization of the core and the periphery-core linkage.