Abstract
Our work here is to propose a novel technique by which chaos complete and phase synchronizations can be accomplished via a low-cost scheme. We call the proposed technique a "single-state feedback track synchronization control algorithm". A single-state feedback track synchronization control algorithm is designed so that both complete and phase synchronizations can be accomplished using the same controller. Complete synchronization between two chaotic systems means complete symmetry between them, but phase synchronization means complete symmetry with a phase shift. In addition, the proposed method is applied to the synchronization of two identical chaotic Lorenz models. The effectiveness and robustness of the proposed algorithm is well illustrated via exhaustive numerical simulation experiments based on the Matlab toolbox of the powerful genetic algorithm. The robustness of the proposed algorithm motivated us to apply this method of synchronization in a secure communication application.