Disordering effects of colour in a system of coupled Brownian motors: phase diagram and anomalous to normal hysteresis transition

A system of periodically coupled nonlinear phase oscillators—submitted to both additive and multiplicative white noises—has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis. These features stem from the asymmetry of the stationary probability distribution function, arising through a noise-induced non-equilibrium phase transition which is re-entrant as a function of the multiplicative noise intensity. Using an explicit mean-field approximation we analyse the effect of the multiplicative noises being coloured, finding a contraction of the ordered phase (and a re-entrance as a function of the coupling) on one hand, and a shift of the transition from anomalous to normal hysteresis inside this phase on the other.