Effect of colored noise on networks of nonlinear oscillators.

We discuss noise-induced pattern formation in different two-dimensional networks of nonlinear oscillators, namely a sequence of biochemical reactions and the Lorenz system. The main focus of the work is on the dependence of these patterns on the correlation time (i.e., the color) of exponentially correlated Gaussian noise. It is seen that in the nonchaotic case, the homogeneity (or average cluster size) goes through a minimum with higher correlation time, while in its chaotic regime the Lorenz system shows a higher degree of synchronization when the correlation time of the noise is increased. In order to elucidate the origin of this phenomenon, the effect of colored noise on the individual oscillator is investigated. It is shown that the specific dependence of the network's homogeneity on the noise correlation time arises from an interplay of the collective behavior and the properties of the single oscillators.