Amplitude death in networks of delay-coupled delay oscillators

TL;DR

This paper investigates amplitude death in networks of delay-coupled delay oscillators, deriving analytical conditions for its occurrence and demonstrating its presence in both homogeneous and heterogeneous networks.

Contribution

It provides the first analytical framework linking network eigenvalues to amplitude death in delay-coupled delay oscillators, including large coupling strengths.

Findings

Amplitude death occurs at large coupling strengths regardless of coupling delay.

Small coupling delays scaled with 1/k can induce amplitude death.

Results extend from homogeneous to heterogeneous network structures.

Abstract

Amplitude death is a dynamical phenomenon in which a network of oscillators settles to a stable state as a result of coupling. Here, we study amplitude death in a generalized model of delay-coupled delay oscillators. We derive analytical results for degree homogeneous networks that show that amplitude death is governed by certain eigenvalues of the network's adjacency matrix. In particular these results demonstrate that in delay-coupled delay oscillators amplitude death can occur for arbitrarily large coupling strength k. In this limit we find a region of amplitude death, which occurs already at small coupling delays that scale with 1/k. We show numerically that these results remain valid in random networks with heterogeneous degree distribution.