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Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters

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Abstract

This paper focuses on the adaptive modified hybrid function projective synchronization with complex function transformation matrix (CMHFPS) for different dimensional chaotic (hyperchaotic) systems with complex variables and unknown complex parameters. The chaotic systems are considerably different from those in the existing closely related literature. Moreover, the transformation matrix in this type of chaos synchronization is not a square matrix, and its elements are complex functions. In particular, by constructing appropriate Lyapunov functions dependent on complex variables, the adaptive controllers are designed to synchronize different dimensional complex chaos (hyperchaos) with complex parameters in the sense of CMHFPS, and the complex update laws for estimating unknown complex parameters of complex chaotic systems are also given. Finally, two examples are presented to illustrate the effectiveness and feasibility of the theoretical results.

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Acknowledgments

The authors are very grateful to the editors and the reviewers for their constructive comments and suggestions. This research was supported in part by the National Nature Science Foundation of China (Grant Nos. 61273088, 61473133, 61533011), the Nature Science Foundation of Shandong Province, China (No. ZR2014FL015), Doctoral Research Foundation of University of Jinan (No. XBS1531) and the Foundation for University Young Key Teacher Program of Shandong Provincial Education Department, China.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Ji’nan, Jinan, 250022, Shandong, People’s Rupublic of China

    Jian Liu

  2. School of Control Science and Engineering, Shandong University, Jinan, 250061, Shandong, People’s Rupublic of China

    Shutang Liu

  3. Department of Physics, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Julien Clinton Sprott

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  1. Jian Liu
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  2. Shutang Liu
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  3. Julien Clinton Sprott
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Correspondence to Jian Liu.

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Liu, J., Liu, S. & Sprott, J.C. Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters. Nonlinear Dyn 83, 1109–1121 (2016). https://doi.org/10.1007/s11071-015-2391-8

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  • DOI: https://doi.org/10.1007/s11071-015-2391-8

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