Noiseless Collective Motion out of Noisy Chaos

We consider the effect of microscopic external noise on the collective motionof a globally coupled map in fully desynchronized states. Without the externalnoise a macroscopic variable shows high-dimensional chaos distinguishable fromrandom motion. With the increase of external noise intensity, the collectivemotion is successively simplified. The number of effective degrees of freedomin the collective motion is found to decrease as $-\log{\sigma^2}$ with theexternal noise variance $\sigma^2$. It is shown how the microscopic noise cansuppress the number of degrees of freedom at a macroscopic level.Comment: 9 pages RevTex file and 4 postscript figure