  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
nonequilibrium phase transition which is "reentrant" as a function of the
multiplicative noise intensity. Using an explicit mean-field approximation we
analyze the effect of the multiplicative noises being coloured, finding a
contraction of the ordered phase (and a reentrance 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.
