Occasional coupling enhances amplitude death in delay-coupled oscillators

TL;DR

This paper demonstrates that occasional (intermittent) coupling significantly enlarges the amplitude death regions in delay-coupled oscillators, including limit cycle, chaotic, and thermoacoustic systems, through analytical and numerical analysis.

Contribution

It introduces and validates the effectiveness of occasional coupling schemes in enhancing amplitude death in various delay-coupled oscillators, including practical thermoacoustic models.

Findings

Occasional coupling enlarges amplitude death regions compared to continuous coupling.

Analytical stability analysis explains the enhancement mechanism.

Similar effects observed with practical wave-based coupling functions.

Abstract

This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies the intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart-Landau) and coupled chaotic oscillators (R\"ossler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on-off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time-delay coupled oscillators and get similar results.