Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators

TL;DR

This paper investigates the synchronization and stability properties of coupled Helmholtz-Duffing oscillators in bi-stability regimes, revealing complex spatial configurations and differing stability despite identical parameters.

Contribution

It provides new insights into the stability and spatial patterns of coupled nonlinear oscillators under bi-stability conditions.

Findings

Different stability of states despite identical parameters.

Final stable states have diverse spatial configurations.

Stability depends on spatial perturbation modes.

Abstract

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.