Coupled Dynamics on Networks

TL;DR

This paper investigates how coupled nonlinear dynamical systems on networks synchronize, revealing phenomena like floating nodes and two distinct cluster formation mechanisms as coupling strength varies.

Contribution

It introduces the concepts of floating nodes and distinguishes between self-organized and driven cluster formations in network synchronization.

Findings

Nodes form synchronized clusters as coupling increases.

Floating nodes intermittently attach and detach from clusters.

Two mechanisms of cluster formation identified: self-organized and driven.

Abstract

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the network. For small coupling strengths nodes show turbulent behavior but form synchronized clusters as coupling increases. When nodes show synchronized behaviour, we observe two interesting phenomena. First, there are some nodes of the floating type that show intermittent behaviour between getting attached to some clusters and evolving independently. Secondly, we identify two different ways of cluster formation, namely self-organized clusters which have mostly intra-cluster couplings and driven clusters which have mostly inter-cluster couplings.