| Summary: | In this paper, we review the complicated (or complex) lag (or slack) synchronization (CLS) of coupled complex chaotic nonlinear structures with unknown parameters. In spite of its unusual properties, the significance of CLS is yet to be fully demonstrated in the literature. Using a Lyapunov function, an adaptive (or versatile) controller is developed to synchronize coupled, generally unknown chaotic complex structures. This enables the uncertain parameters of the structures to be evaluated. The CLS of indistinguishable twin complex Lü structures is recognized as a simulation pattern. A number of results demonstrate the state characteristics, modulus errors, and phase errors for these chaotic attractors following the onset of CLS, thus verifying the theoretical derivations. CLS is an encouraging phenomenon, as the synchronization between the state characteristics of the principal structure and those of the slave structure enable excellent communication security. Numerical simulations of secure communications demonstrate the transmission of an encrypted message and an image signal. Keywords: Complex lag synchronization, Chaotic structures, Unknown, Secure communications, Lyapunov function, Complex
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