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The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters

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Abstract

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule and a proper Lyapunov candidate function, the unknown coefficients of the system are estimated and the stabilization of the synchronizer system is demonstrated. Finally, the numerical simulation illustrates the efficiency of the proposed method in synchronizing two chaotic systems.

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Notes

  1. * Figures 1–4 can be accessed from http://www.ias.ac.in/pramana/v86/supplement.pdf.

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Authors and Affiliations

  1. Department of Electrical Engineering, Gonabad Branch, Islamic Azad University, Gonabad/Khorasan-e-Razavi, Iran

    ADELEH NOURIAN & SAEED BALOCHIAN

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  1. ADELEH NOURIAN
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  2. SAEED BALOCHIAN
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Correspondence to SAEED BALOCHIAN.

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NOURIAN, A., BALOCHIAN, S. The adaptive synchronization of fractional-order Liu chaotic system with unknown parameters. Pramana - J Phys 86, 1401–1407 (2016). https://doi.org/10.1007/s12043-015-1178-2

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  • DOI: https://doi.org/10.1007/s12043-015-1178-2

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