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Combination–combination synchronization among four identical or different chaotic systems

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Abstract

Based on one drive system and one response system synchronization model, a new type of combination–combination synchronization is proposed for four identical or different chaotic systems. According to the Lyapunov stability theorem and adaptive control, numerical simulations for four identical or different chaotic systems with different initial conditions are discussed to show the effectiveness of the proposed method. Synchronization about combination of two drive systems and combination of two response systems is the main contribution of this paper, which can be extended to three or more chaotic systems. A universal combination of drive systems and response systems model and a universal adaptive controller may be designed to our intelligent application by our synchronization design.

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Acknowledgements

The authors thank the editor and the anonymous reviewers for their resourceful and valuable comments and constructive suggestions. The work is supported the State Key Program of National Natural Science of China (Grant No. 61134012), the National Science Foundation of China (Grant Nos. 60970084, 61070238), Basic and Frontier Technology Research Program of Henan Province (Grant No. 122300413211), the Distinguished Talents Program of Henan Province (Grant No. 124200510017), China Postdoctoral Science Foundation funded project under Grant 2012M511615.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Hubei, 430074, China

    Junwei Sun, Yi Shen, Guodong Zhang & Chengjie Xu

  2. Key Laboratory of Ministry of Education for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Hubei, 430074, China

    Junwei Sun, Yi Shen, Guodong Zhang & Chengjie Xu

  3. Henan Key Lab of Information-based Electrical Appliances, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Junwei Sun & Guangzhao Cui

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  1. Junwei Sun
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  2. Yi Shen
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  3. Guodong Zhang
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  4. Chengjie Xu
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  5. Guangzhao Cui
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Correspondence to Yi Shen.

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Sun, J., Shen, Y., Zhang, G. et al. Combination–combination synchronization among four identical or different chaotic systems. Nonlinear Dyn 73, 1211–1222 (2013). https://doi.org/10.1007/s11071-012-0620-y

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  • DOI: https://doi.org/10.1007/s11071-012-0620-y

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