Noise-Induced Phase Bistability via Stochastic Rocking

We study the effect of a randomly modulated harmonic driving on the phase behavior of a nonlinear oscillator. A multiple-scale analysis shows that the system is formally equivalent to a rocked oscillator, in which a modulated harmonic driving locks the system at one of two phases, both of which are in quadrature with that of the driving. This theoretically predicted noise-induced bistable phase locking is reproduced with numerical simulations of a stochastic Stuart-Landau model, and verified experimentally in a nonlinear electronic circuit.