Transition to amplitude death in scale-free networks

TL;DR

This paper studies how increasing coupling strength causes a transition to amplitude death in scale-free networks, revealing a three-stage process involving hierarchical node death and cluster elimination.

Contribution

It introduces a detailed three-stage framework describing the transition to amplitude death in scale-free networks of nonlinear oscillators.

Findings

Identification of a three-stage transition process

Hierarchical death of amplitude stairs observed

Complete amplitude death achieved through cluster and node elimination

Abstract

Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated. As the coupling strength increases, the network will undergo three stages in approaching to the state of complete amplitude death. The first stage is featured by a \emph{"stair-like"} distribution of the node amplitude, and the transition is accomplished by a \emph{hierarchical death} of the amplitude stairs. The second and third stages are characterized by, respectively, a continuing elimination of the synchronous clusters and a fast death of the non-synchronized nodes.