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The adaptive synchronization of fractional-order chaotic system with fractional-order \(\varvec{1}<\varvec{q}<\varvec{2}\) via linear parameter update law

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Abstract

This paper presents an adaptive synchronization approach for fractional-order chaotic systems with fractional-order \(1<q<2\) and unknown system parameters based on the Mittag–Leffler function and the generalized Gronwall inequality. A sufficient condition is obtained. The numerical simulations are given to verify the effectiveness of this synchronization scheme.

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Acknowledgments

We are very grateful to the reviewers for their valuable comments and suggestions. This work is supported in part by the National Natural Science Foundation of China (61104150), Science Fund for Distinguished Young Scholars of Chongqing (cstc2013jcyjjq40001), the Science and Technology Project of Chongqing Education Commission (KJ130517) and Natural Science Foundation of Chongqing (cstc2013jcyjA00026).

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Authors and Affiliations

  1. Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Ping Zhou & Rongji Bai

  2. Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Ping Zhou & Rongji Bai

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  1. Ping Zhou
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  2. Rongji Bai
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Correspondence to Ping Zhou.

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Zhou, P., Bai, R. The adaptive synchronization of fractional-order chaotic system with fractional-order \(\varvec{1}<\varvec{q}<\varvec{2}\) via linear parameter update law. Nonlinear Dyn 80, 753–765 (2015). https://doi.org/10.1007/s11071-015-1903-x

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  • DOI: https://doi.org/10.1007/s11071-015-1903-x

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