Transition from the self-organized to the driven dynamical clusters

TL;DR

This paper investigates how synchronized clusters form in coupled map networks, revealing the transition from self-organized to driven clusters influenced by coupling strength and network topology, with Lyapunov analysis elucidating the underlying dynamics.

Contribution

It introduces a detailed analysis of cluster formation mechanisms in coupled maps, highlighting the transition between self-organized and driven clusters based on network rewiring and coupling strength.

Findings

Driven clusters are independent of network rewiring at low coupling.

Transition from self-organized to driven clusters occurs at higher coupling strengths.

Lyapunov analysis explains the dynamical origin of cluster formation.

Abstract

We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self- synchronized or driven-synchronized, based on the coupling strength and underlying network structures. A smaller coupling strength region shows driven clusters independent of the network rewiring strategies, whereas a larger coupling strength region shows the transition from the self-organized cluster to the driven cluster as network connections are rewired to the bi-partite type. Lyapunov function analysis is performed to understand the dynamical origin of cluster formation. The results provide insights into the relationship between the topological clusters which are based on the direct connections between the nodes, and the dynamical clusters which are based on the functional behavior of these nodes.