Amplitude Death: The cessation of oscillations in coupled nonlinear dynamical systems

TL;DR

This paper reviews the phenomenon of amplitude death in coupled nonlinear systems, exploring mechanisms, phase-flip transitions, and recent advances in understanding how oscillations cease due to interactions.

Contribution

It provides a comprehensive summary of recent research on amplitude death, including new insights into underlying mechanisms and transient dynamics effects.

Findings

Identification of mechanisms leading to amplitude death

Analysis of phase-flip transition in transient dynamics

Enhanced understanding of oscillation suppression in nonlinear systems

Abstract

Here we extend a recent review (Physics Reports {\bf 521}, 205 (2012)) of amplitude death, namely the suppression of oscillations due to the coupling interactions between nonlinear dynamical systems. This is an important emergent phenomenon that is operative under a variety of scenarios. We summarize results of recent studies that have significantly added to our understanding of the mechanisms that underlie the process, and also discuss the phase--flip transition, a characteristic and unusual effect that occurs in the transient dynamics as the oscillations die out.