Diversity-induced resonance in a system of globally coupled linear oscillators

TL;DR

This paper investigates how diversity in parameters like mass, frequency, and damping among coupled linear oscillators can lead to resonance phenomena, highlighting the role of synchronization induced by coupling.

Contribution

It provides a detailed analysis of diversity-induced resonance in a simple, analytically tractable model of globally coupled linear oscillators with explicit conditions for resonance.

Findings

Resonance occurs when oscillator diversity and coupling induce synchronization.

A steady state solution for the system is derived.

Conditions for the emergence of resonance are identified.

Abstract

The purpose of this paper to analyze in some detail the arguably simplest case of diversity-induced reseonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters characterizing each oscillator, namely its mass, internal frequency and damping coefficient are drawn from a probability distribution. The main ingredients for the diversity-induced-resonance phenomenon are present in this system as the oscillators display a variability in the individual responses but are induced, by the coupling, to synchronize their responses. A steady state solution for this model is obtained. We also determine the conditions under which it is possible to find a resonance effect.