  We show how two electrically coupled semiconductor lasers having optical
feedback can present simultaneous anti-phase correlated fast power
fluctuations, and strong in-phase synchronized spikes of chaotic power drops.
This quite counter intuitive phenomenon is demonstrated experimentally and
confirmed by numerical solutions of a deterministic dynamical system of rate
equations. The occurrence of negative and positive cross correlation between
parts of a complex system according to time scales, as proved in our simple
arrangement, is relevant for the understanding and characterization of
collective properties in complex networks.
