Multistability of globally coupled Duffing oscillators

TL;DR

This paper investigates how globally coupled Duffing oscillators can exhibit multistability due to bistability at the individual level, analyzing the conditions for cluster formation and full synchronization.

Contribution

It provides a combined analytical and numerical study of the existence and stability of two-cluster solutions in coupled Duffing oscillators, revealing how coupling strength influences collective states.

Findings

Multistability arises from bistability of individual oscillators.

Two-cluster solutions dominate at intermediate coupling strengths.

Full synchronization occurs as coupling strength increases.

Abstract

We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators. The multiplicity of these solutions, induced by the many possible ways of distributing the oscillators between the two clusters, implies that the ensemble can exhibit multistability. As the strength of coupling grows, however, the two-cluster solutions are replaced by a state of full synchronization. By a combination of analytical and numerical techniques, we study the existence and stability of two-cluster solutions. The role of the distribution of oscillators between the clusters and the relative prevalence of the two stable solutions are disclosed.