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Hybrid Chaos Synchronization of Liu and Lü Systems by Active Nonlinear Control

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Trends in Computer Science, Engineering and Information Technology (CCSEIT 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 204))

Abstract

This paper investigates the hybrid chaos synchronization of identical Liu systems, identical Lü systems, and non-identical Liu and Lü systems by active nonlinear control. Liu system (Liu et al. 2004) and Lü system (Lü and Chen, 2002) are important models of three-dimensional chaotic systems. Hybrid synchronization of the three-dimensional chaotic systems considered in this paper are achieved through the synchronization of the first and last pairs of states and anti-synchronization of the middle pairs of the two systems. Sufficient conditions for hybrid synchronization of identical Liu, identical Lü, and non-identical Liu and Lü systems are derived using active nonlinear control and Lyapunov stability theory. Since the Lyapunov exponents are not needed for these calculations, the active nonlinear control is an effective and convenient method for the hybrid synchronization of the chaotic systems addressed in this paper. Numerical simulations are shown to illustrate the effectiveness of the proposed synchronization schemes.

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Author information

Authors and Affiliations

  1. Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University, Avadi-Alamathi Road, Avadi, Chennai, 600 062, India

    Sundarapandian Vaidyanathan

Authors
  1. Sundarapandian Vaidyanathan
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Editors and Affiliations

  1. Wireilla Net Solutions PTY Ltd, Melbourne, Victoria, Australia

    Dhinaharan Nagamalai

  2. Institut Telecom/Telecom SudParis, 91011, 9, rue Charles Fourier, Evry Cedex, France

    Eric Renault

  3. Manonmaniam Sundaranar University, Thirunelveli, Tamil Nadu, India

    Murugan Dhanuskodi

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Vaidyanathan, S. (2011). Hybrid Chaos Synchronization of Liu and Lü Systems by Active Nonlinear Control. In: Nagamalai, D., Renault, E., Dhanuskodi, M. (eds) Trends in Computer Science, Engineering and Information Technology. CCSEIT 2011. Communications in Computer and Information Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24043-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-24043-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24042-3

  • Online ISBN: 978-3-642-24043-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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