Noiseless Collective Motion out of Noisy Chaos

We consider the effect of microscopic external noise on the collective motion of a globally coupled map in fully desynchronized states. Without the external noise a macroscopic variable shows high-dimensional chaos distinguishable from random motion. With the increase of external noise intensity, the collective motion is successively simplified. The number of effective degrees of freedom in the collective motion is found to decrease as $-\log {\sigma }^2$ with the external noise variance ${\sigma }^2$. It is shown how the microscopic noise can suppress the number of degrees of freedom at a macroscopic level.