COLLECTIVE CHAOS AND NOISE IN THE GLOBALLY COUPLED COMPLEX GINZBURG-LANDAU EQUATION

We study a globally coupled version of the complex Ginzburg-Landau equ ation (GC-CGLE) which consists of a large number N of identical two-di mensional oscillators coupled through their mean amplitude, Depending on parameter values, different dynamical regimes are attained. We focu s particularly on an interesting regime where the individual oscillato rs follow erratic motion but in a sufficiently coherent way so that th e average motion does not vanish when N becomes large and is also chao tic. A simple description of this state is proposed by considering the motion of a single forced two-dimensional system which has both a lim it cycle and a fixed point as stable attractors. Determining which of these two deterministic attractors is selected by a weak noise and how this depends on the parameter of the reduced system allows us to dete rmine self-consistently the average amplitude and dominant frequency o f the collective behaviour of the full system. Finally, we show that a dding a small noise to the GC-CGLE transforms the chaotic collective b ehaviour into a purely periodic one.