Paths to Synchronization on Complex Networks

TL;DR

This paper explores how local synchronization patterns develop differently in homogeneous and heterogeneous complex networks, revealing how coupling strength and topology influence the path to global synchronization.

Contribution

It introduces new insights and tools to understand the influence of network topology and coupling strength on synchronization pathways.

Findings

Local synchronization patterns differ between homogeneous and heterogeneous networks.

The path to global synchronization depends on network topology and coupling strength.

Different emergent behaviors are observed based on network structure.

Abstract

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this paper, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.