¹Henan Institute of Science and Technology, Xinxiang 453003, China
²Xinxiang Medical University, Xinxiang 453003, China

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Abstract—The dynamic behavior of fractional order systems have received increasing attention in recent years, In this paper the reliable phase synchronization problem between two coupled chaotic fractional order system with varying time is constructed, An active delay expected synchronization between two coupled chaotic fractional order systems and hyperchaotic fractional order systems is analyzed by utilizing Laplace transform. Furthermore, we investigated the necessary conditions for fractional order Rossler systems to exhibit chaotic attractor. Then, based on the stability results of fractional order systems, sufficient conditions for phase synchronization of the fractional models of Rossler systems and hyperchaotic system are derived. The synchronization scheme that is simple and global enabled synchronization of fractional order chaotic systems to be achieved, Theory analysis and corresponding numerical simulations results show that the chaos in such fractional order system with varying time delay can be synchronized and the method is effective and feasible.

Index Terms—Autonomous system, the expected synchronization, fractional order, high dimension.

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Cite: Wenxian Xiao, Zhen Liu, Wenlong Wan, Xiali Zhao, "Research on the Expected Synchronization of Autonomous System," Journal of Software vol. 8, no. 1, pp. 85-92, 2013.