Zero-lag long-range synchronization via dynamical relaying

We show that simultaneous synchronization between two delay-coupled oscillators can be achieved by relaying the dynamics via a third mediating element, which surprisingly lags behind the synchronized outer elements. The zero-lag synchronization thus obtained is robust over a considerable parameter range. We substantiate our claims with experimental and numerical evidence of these synchronization solutions in a chain of three coupled semiconductor lasers with long inter-element coupling delays. The generality of the mechanism is validated in a neuronal model with the same coupling architecture. Thus, our results show that synchronized dynamical states can occur over long distances through relaying, without restriction by the amount of delay.