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Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters

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Abstract

This paper introduces a new type of synchronization method of adaptive modified projective synchronization with complex scaling matrix (ACMPS) for two \(n\)-dimensional complex chaotic (hyperchaotic) systems with uncertain complex parameters. By choosing appropriate Lyapunov functions dependent on complex variables, and employing adaptive control technique, sufficient criteria on ACMPS are derived. Moreover, in the complex space, the slave system can be asymptotically synchronized up to nonidentical or identical master system by a desired complex scaling matrix, and all of unknown parameters in both master and slave systems are achieved to be identified by virtue of the complex update laws. Finally, two examples are worked out to verify the effectiveness and feasibility of the theoretical results.

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Acknowledgments

This research was partially supported by the National Nature Science Foundation of China (Grant Nos. 61273088, 61473133), the Nature Science Foundation of Shandong Province, China (Grant No. ZR2011AL007). The authors would like to thank the editors and the reviewers for their constructive comments and suggestions, which improved the quality of the paper.

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Authors and Affiliations

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

    Jian Liu & Shutang Liu

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

    Jian Liu & Chunhua Yuan

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  1. Jian Liu
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  2. Shutang Liu
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  3. Chunhua Yuan
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Correspondence to Jian Liu.

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Liu, J., Liu, S. & Yuan, C. Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters. Nonlinear Dyn 79, 1035–1047 (2015). https://doi.org/10.1007/s11071-014-1721-6

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  • DOI: https://doi.org/10.1007/s11071-014-1721-6

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