General mechanism for amplitude death in coupled systems

TL;DR

This paper presents a universal mechanism for inducing amplitude death in coupled dynamical systems through a combination of direct and indirect feedback couplings, supported by stability analysis and diverse system examples.

Contribution

It introduces a general framework explaining how amplitude death can occur via competing synchronization and anti-synchronization effects in coupled systems.

Findings

Amplitude death can be induced by sufficient indirect feedback coupling.

Transitions to amplitude death can be continuous or discontinuous.

The mechanism applies to various dynamics and coupling types.

Abstract

We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling through an environment or an external system is introduced in them, it is found to induce a tendency for anti-synchronization. We show that, for sufficient strengths, these two competing effects can lead to amplitude death. We provide a general stability analysis that gives the threshold values for onset of amplitude death. We study in detail the nature of the transition to death in several specific cases and find that the transitions can be of two types - continuous and discontinuous. By choosing a variety of dynamics for example, periodic, chaotic, hyper chaotic, and time-delay systems, we illustrate that this mechanism is quite general and works for different types of direct coupling, such as diffusive, replacement, and synaptic couplings and for different damped dynamics of the environment.