Transition from amplitude to oscillation death in a network of oscillators

TL;DR

This paper investigates how a network of identical oscillators transitions from a homogeneous steady state to inhomogeneous steady states, revealing the roles of negative mean field links and coupling strength in this process.

Contribution

It analytically and numerically demonstrates the transition mechanisms from amplitude to oscillation death in oscillator networks, including the effects of negative mean field links.

Findings

Network splits into two clusters with negative mean field links.

Transition from HSS to IHSS depends on coupling strength and number of negative links.

Transitions involve bifurcations similar to Turing patterns.

Abstract

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population in the network with a few local negative mean field links. It is observed that the whole population splits into two clusters for a certain number of negative mean field links and specific range of coupling strength. For further increases of the strength of interaction these clusters collapse to a HSS followed by a transition to IHSSs. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of negative mean-field links and the strength of interaction using a reductionism approach to the model network in a two-cluster state. We verify the results with numerical examples of networks using the paradigmatic Landau-Stuart limit cycle system and the chaotic Rossler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.