Mutual synchronization and clustering in randomly coupled chaotic dynamical networks

TL;DR

This paper investigates how the connectivity and architecture of randomly coupled chaotic maps influence synchronization and clustering, revealing phase transitions and hierarchical structures in the system.

Contribution

It introduces a model of randomly coupled maps and analyzes the effects of connectivity and architecture on synchronization and clustering patterns.

Findings

Global synchronization occurs below a critical connectivity threshold.

Cluster structures depend on coupling architecture.

Hierarchical clustering and emerging graphs are observed.

Abstract

We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally coupled maps) until a certain critical threshold for the connectivity is reached. We further show that not only the average connectivity, but also the architecture of the couplings is responsible for the cluster structure observed. We analyse the different phases of the system and use various correlation measures in order to detect ordered non-synchronized states. Finally, it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs.