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Compound synchronization for four chaotic systems of integer order and fractional order

By combining the tracking control and the stability theory of nonlinear fractional-order systems, a novel kind of compound synchronization among four chaotic systems of integer order and fractional order has been investigated, where the drive systems have been conceptually divided into two categories: the scaling drive system and the base drive system. A fractional-order chaotic system can realize compound synchronization with the novel system, which is a combination system among two integer-order chaotic systems and one different fractional-order chaotic system. Numerical simulation results are presented to demonstrate the effectiveness and correctness of the compound synchronization.