  A bifurcating system subject to multiplicative noise can display on-off
intermittency. Using a canonical example, we investigate the extreme
sensitivity of the intermittent behavior to the nature of the noise. Through a
perturbative expansion and numerical studies of the probability density
function of the unstable mode, we show that intermittency is controlled by the
ratio between the departure from onset and the value of the noise spectrum at
zero frequency. Reducing the noise spectrum at zero frequency shrinks the
intermittency regime drastically. This effect also modifies the distribution of
the duration that the system spends in the off phase. Mechanisms and
applications to more complex bifurcating systems are discussed.

Statistical Mechanics