Patterns and stability of coupled multi-stable nonlinear oscillators

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.

Automated summary

Nonlinear oscillators and their synchronization have been extensively studied. This study focuses on the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. The results show that the stability of the two states to spatial perturbations is different, and the final stable states are determined by both the wavelength of the perturbing mode and the coupled oscillator phases.