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Analysis, Control and Synchronization of Hyperchaotic Zhou System via Adaptive Control

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Advances in Computing and Information Technology

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 177))

Abstract

This paper investigates the analysis, control and synchronization of the hyperchaotic Zhou system (2009) via adaptive control. First, an adaptive control scheme is derived to stabilize the hyperchaotic Zhou system with unknown parameters to its unstable equilibrium at the origin. Then an adaptive synchronization scheme is derived to achieve global chaos synchronization of the identical hyperchaotic Zhou systems with unknown parameters. The results derived for adaptive stabilization and synchronization for the hyperchaotic system are established using the Lyapunov stability theory. Numerical simulations are shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper.

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References

  1. Rössler, O.E.: An equation for hyperchaos. Phys. Lett. A 71, 155–157 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ning, C.Z., Haken, H.: Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. Phys. Rev. A 41, 3826–3837 (1990)

    Article  Google Scholar 

  3. Kapitaniak, T., Chua, L.O.: Hyperchaotic attractor of unidirectionally coupled Chua’s circuit. Int. J. Bifurcat. Chaos 4, 477–482 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196–1199 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ge, S.S., Wang, C., Lee, T.H.: Adaptive backstepping control of a class of chaotic systems. Internat. J. Bifur. Chaos 10, 1149–1156 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Sun, M., Tian, L., Jiang, S., Xun, J.: Feedback control and adaptive control of the energy resource chaotic system. Chaos, Solitons & Fractals 32, 168–180 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  8. Lu, L., Zhang, C., Guo, Z.A.: Synchronization between two different chaotic systems with nonlinear feedback control. Chinese Physics 16(6), 1603–1607 (2007)

    Article  Google Scholar 

  9. Sundarapandian, V.: Hybrid chaos synchronization of hyperchaotic Liu and hyperchaotic Chen systems by active nonlinear control. Internat. J. Computer Sci. Eng. Inform. Tech. 1(2), 1–14 (2011)

    Article  Google Scholar 

  10. Liao, T.L., Tsai, S.H.: Adaptive synchronization of chaotic systems and its applications to secure communications. Chaos, Solitons & Fractals 11, 1387–1396 (2000)

    Article  MATH  Google Scholar 

  11. Sundarapandian, V.: Adaptive synchronization of hyperchaotic Lorenz and hyperchaotic Lü systems. Internat. J. Instrument. Control Sys. 1(1), 1–18 (2011)

    Google Scholar 

  12. Sundarapandian, V.: Adaptive stabilization and synchronization of Lü-like chaotic attractor. Internat. J. Comp. Sci. Eng. Informat. Tech. 1(4), 15–26 (2011)

    Google Scholar 

  13. Yang, T., Chua, L.O.: Control of chaos using sampled-data feedback control. Internat. J. Bifur. Chaos 9, 215–219 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yu, Y.G., Zhang, S.C.: Adaptive backstepping synchronization of uncertain chaotic systems. Chaos, Solitons & Fractals 27, 1369–1375 (2006)

    Article  MathSciNet  Google Scholar 

  15. Konishi, K., Hirai, M., Kokame, H.: Sliding mode control for a class of chaotic systems. Phys. Lett. A 245, 511–517 (1998)

    Article  Google Scholar 

  16. Sundarapandian, V.: Global chaos synchronization of Pehlivan systems by sliding mode control. Internat. J. Comp. Sci. Eng. 3(5), 2163–2169 (2011)

    Google Scholar 

  17. Zhou, P., Cao, Y.X., Cheng, X.F.: A new hyperchaos system and its circuit simulation by EWB. Chinese Physics B 18(4), 1394–1398 (2009)

    Article  Google Scholar 

  18. Hahn, W.: The Stability of Motion. Springer, New York (1967)

    Google Scholar 

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Author information

Authors and Affiliations

  1. R & D 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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Correspondence to Sundarapandian Vaidyanathan .

Editor information

Editors and Affiliations

  1. , Department of Computer Science, Jackson State University, John R. Lynch Street 1400, Jackson, 39217, USA

    Natarajan Meghanathan

  2. Wireilla Net Solutions PTY Ltd, Melbourne, Australia

    Dhinaharan Nagamalai

  3. Department of Computer Science & Eng., University of Calcutta, Calcutta, 700 073, India

    Nabendu Chaki

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Vaidyanathan, S. (2013). Analysis, Control and Synchronization of Hyperchaotic Zhou System via Adaptive Control. In: Meghanathan, N., Nagamalai, D., Chaki, N. (eds) Advances in Computing and Information Technology. Advances in Intelligent Systems and Computing, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31552-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-31552-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31551-0

  • Online ISBN: 978-3-642-31552-7

  • eBook Packages: EngineeringEngineering (R0)

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