Noise-induced transitions between attractors in time periodically driven systems

The stochastic Landau equation for a periodically driven process with either two discretely degenerate attractors or a continuum of degenerate attractors is studied for small noise. We calculate analytically the probability ${\mathit{P}}^{\mathrm{tr}}$ for the transition between the attractors leading to phase diffusion in the continuous case. Our results are in good agreement with numerical simulations and in the discrete case also with experiments on periodically driven Rayleigh-Bénard convection. They explain the sensitive dependence of ${\mathit{P}}^{\mathrm{tr}}$ on the equation’s parameters.