Unfolding Substructures of Complex Networks by Coupling Chaotic Oscillators beyond Global Synchronization Regime

TL;DR

This paper shows that by tuning the coupling strength of chaotic oscillators on complex networks, one can reveal the network's hierarchical substructures beyond traditional synchronization methods, offering new insights into network organization.

Contribution

It introduces a novel approach to uncover hierarchical community structures in complex networks using partial synchronization of chaotic oscillators outside the stable synchronization regime.

Findings

Nodes within the same hierarchical component cluster tightly.

Different hierarchy levels can be systematically unfolded.

Method is effective for detecting hierarchical community structures.

Abstract

In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable region, i.e., global synchronization. In this letter, we demonstrate that synchronization process on complex networks can efficiently reveal the substructures of networks when the coupling strength of chaotic oscillators is under the lower boundary of stable region. Both analytic and numerical results show that the nodes belonging to the same component in the hierarchical network are tightly clustered according to the Euclidean distances between the state vectors of the corresponding oscillators, and different levels of hierarchy can be systematically unfolded by gradually tuning the coupling strength. When the coupling strengths exceed the upper boundary of stable region, the hierarchy of the network cannot be recognized by this approach. Extensive simulations suggest that our method may provide a powerful tool to detect the hierarchical community structure of complex systems and deep insight into the relationship between structure and dynamics of complex systems.