Zero lag synchronization of chaotic systems with time delayed couplings

Zero-lag synchronization (ZLS) between chaotic units, which do not have self-feedback or a relay unit connecting them, is experimentally demonstrated for two mutually coupled chaotic semiconductor lasers. The mechanism is based on two mutual coupling delay times with certain allowed integer ratios, whereas for a single mutual delay time ZLS cannot be achieved. This mechanism is also found numerically for mutually coupled chaotic maps where its stability is analyzed using the Schur-Cohn theorem for the roots of polynomials. The symmetry of the polynomials allows only specific integer ratios for ZLS. In addition, we present a general argument for ZLS when several mutual coupling delay times are present.