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Rate Estimation of Identical Synchronization by Designing Controllers

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  • Mitul Islam
  • Bipul Islam
  • Nurul Islam

Abstract

This paper investigates the synchronization rate for identical synchronization of chaotic dynamical systems, achieved by using controllers. The paper stresses on the hybrid feedback control technique and the tracking control technique and determines their corresponding maximum, minimum, and average synchronization rates. The results obtained are applied on the Shimizu-Morioka chaotic system, and some necessary and sufficient conditions for synchronization are obtained. Comparison of the two controllers is undertaken on the basis of their synchronization rates, in the context of the Shimizu-Morioka system. The results are analyzed both theoretically and numerically. Moreover, a method of graphical analysis is proposed to completely characterize the set of hybrid controllers for a given system.

Suggested Citation

  • Mitul Islam & Bipul Islam & Nurul Islam, 2013. "Rate Estimation of Identical Synchronization by Designing Controllers," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, May.
    • Handle: RePEc:hin:jjmath:590462
    DOI: 10.1155/2013/590462
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    References listed on IDEAS

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    1. Xiong, Xiaohua & Hong, Shangnan & Wang, Junwei & Gan, Dengwen, 2007. "Synchronization rate of synchronized coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 689-699.
    2. Park, Ju H., 2005. "Controlling chaotic systems via nonlinear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1049-1054.
    3. Sun, Yonghui & Cao, Jinde, 2007. "Adaptive synchronization between two different noise-perturbed chaotic systems with fully unknown parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 253-265.
    4. Yang, Li-Xin & Chu, Yan-Dong & Zhang, Jian-Gang & Li, Xian-Feng & Chang, Ying-Xiang, 2009. "Chaos synchronization in autonomous chaotic system via hybrid feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 214-223.
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