Zero-lag synchronization and multiple time delays in two coupled chaotic systems

Zero-lag synchronization (ZLS) between two chaotic systems coupled by a portion of their signal is achieved for restricted ratios between the delays of the self-feedback and the mutual coupling. We extend this scenario to the case of a set of multiple self-feedbacks {N di} and a set of multiple mutual couplings {N cj}. We demonstrate both analytically and numerically that ZLS can be achieved when σ li N di + σ mj N cj =0, where li, mj Z. Results which were mainly derived for Bernoulli maps and exemplified with simulations of the Lang-Kobayashi differential equations, indicate that ZLS can be achieved for a continuous range of mutual coupling delay. This phenomenon has an important implication in the possible use of ZLS in communication networks.