Signal amplification by unidirectional coupling of oscillators

TL;DR

This paper investigates how unidirectional coupling of monostable Duffing oscillators can amplify weak signals, identifying conditions for undamped propagation and analyzing effects of oscillator number and dimensionality.

Contribution

It introduces a perturbation theory-based approach to analyze signal amplification in unidirectionally coupled Duffing oscillators, including in two-dimensional random coupling scenarios.

Findings

Conditions for undamped signal propagation identified.

Response amplitude approaches a limit as oscillator number increases.

Signal amplification persists in two-dimensional random coupling.

Abstract

We report our investigation on the input signal amplification in unidirectionally coupled monostable Duffing oscillators in one- and two-dimensions with first oscillator alone driven by a weak periodic signal. Applying a perturbation theory we obtain a set of nonlinear equations for the response amplitude of the coupled oscillators. We identify the conditions for undamped signal propagation with enhanced amplitude through the coupled oscillators. When the number of oscillators increases the response amplitude approaches a limiting value. We determine this limiting value. Also, we analyse the signal amplification in the coupled oscillators in two-dimensions with fraction of oscillators chosen randomly for coupling and forcing.