  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.
