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Exponential synchronization of two totally different chaotic systems based on a unified model

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Abstract

This paper presents an exponential synchronization scheme between two chaotic systems with different structures and parameters. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these totally different chaotic systems. A novel state feedback control law is established to exponentially synchronize the two unified models with different parameters. Most chaotic systems with different structures and parameters, such as Hopfield neural networks, cellular neural networks, Chua’s circuits, unified chaotic systems, Qi systems, and chaotic recurrent multilayer perceptrons, can be transformed into this unified model with the synchronization controller designed in a unified way. Two numerical examples are exploited to illustrate the effectiveness of the proposed design schemes.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61174142, 61222310, and 61328302, the Zhejiang Provincial Natural Science Foundation of China under Grant LZ14F030002, the Specialized Research Fund for the Doctoral Program of Higher Education of China (SRFDP) under Grants 20120101110115 and 20130101110109, and the Fundamental Research Funds for the Central Universities under Grant 2014XZZX003-12. This work was also supported by the “151 Talent Project” of Zhejiang Province.

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Authors and Affiliations

  1. State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Meiqin Liu

  2. College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Meiqin Liu, Haiyang Chen, Senlin Zhang & Zhen Fan

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  1. Meiqin Liu
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  2. Haiyang Chen
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  3. Senlin Zhang
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  4. Zhen Fan
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Correspondence to Meiqin Liu.

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Liu, M., Chen, H., Zhang, S. et al. Exponential synchronization of two totally different chaotic systems based on a unified model. Neural Comput & Applic 25, 1801–1808 (2014). https://doi.org/10.1007/s00521-014-1670-5

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  • DOI: https://doi.org/10.1007/s00521-014-1670-5

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