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Synchronization of multiple identical chaotic systems, coupled in a ring structure, was studied in this paper. Ueda attractor was used as an example to perform the synchronization of several chaotic systems. The bound of the Ueda attractor was also estimated by numerical simulation. The above results were also adopted to design a controller to synchronize chaotic systems. The stability of the synchronization of multiple identical chaotic systems was investigated using Lyapunov's direct method. Some sufficient conditions of asymptotical synchronization were attained from rigorous mathematical theory. Further, numerical results were also demonstrated in order to validate the proposed synchronization approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a master-slave synchronization scheme of two n-dimensional nonautonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch. [ABSTRACT FROM AUTHOR]