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Theory of chaos synchronization and quasi-period synchronization of an all optics local area network (O-LAN) is deeply studied and discussed, where two coupled-lasers are used as network’s double-star and the other single-lasers are used as network nodes. The LAN operates double-star lasers to drive node lasers in two links to perform a 2n−D (n is a positive integer, dimensions (D)) laser network. The O-LAN has the characteristics of an all optics LAN with double-center and two link nodes. Our theoretical and numerical results prove that the double-center lasers can obtain their synchronizations with each laser in two link nodes. A route to chaos after a quasi-period bifurcation is analyzed to illustrate dynamics distribution region of O-LAN. We find five quasi-period regions, four chaos regions, where there is a region where instability mixes with the first chaos, and a stable region. We find also that O-LAN can obtain its parallel multi-dynamics synchronizations, such as cycle-one synchronization, cycle-2 synchronization, cycle-3 synchronization, cycle-4 synchronization, cycle-5 synchronization, other quasi-period synchronization and chaos synchronization, shown in two links of O-LAN by shifting the currents of the lasers in one link. The theory of all optics LAN and its obtained results are useful to study on complex dynamic system, optics network, artificial intelligence, chaos and its synchronization.

Theory of chaos synchronization and quasi-period synchronization of an all optic 2n-D LAN