Noise-induced stabilization of collective dynamics

We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is able to stabilize an otherwise linearly unstable collective periodic regime. Microscopic simulations reveal two noise-induced bifurcations of different nature towards self-consistent partial synchrony. We develop a macroscopic treatment solving the corresponding nonlinear Fokker-Planck equation by means of a perturbative approach. The associated linear stability analysis confirms the results anticipated by the numerics. We also argue about the generality of the phenomenon.