Amplitude Death: The emergence of stationarity in coupled nonlinear systems

TL;DR

This paper reviews the phenomenon of amplitude death in coupled nonlinear systems, where oscillations cease and stationary states emerge due to specific coupling strategies, with implications across physics and biology.

Contribution

It provides a comprehensive overview of coupling mechanisms leading to amplitude death and highlights open challenges in understanding this phenomenon.

Findings

Different coupling strategies can induce amplitude death.

Amplitude death stabilizes otherwise unstable fixed points.

Open problems remain in characterizing and controlling AD phenomena.

Abstract

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.