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International Conference on Computational Science, Engineering and Information Technology

CCSEIT 2011: Trends in Computer Science, Engineering and Information Technology pp 84–93Cite as

Global Chaos Synchronization of Hyperchaotic Pang and Wang Systems by Active Nonlinear Control

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

Abstract

This paper investigates the global chaos synchronization of identical hyperchaotic Pang systems (Pang and Liu, 2011) and synchronization of non-identical hyperchaotic Pang system and Wang system (Wang and Liu, 2006). Active nonlinear feedback control is the method used to achieve the synchronization of the identical and different hyperchaotic Pang and Wang systems addressed in this paper and our results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to synchronize identical and different hyperchaotic Pang and Wang systems. Numerical simulations are given to illustrate the effectiveness of the proposed synchronization schemes for the global chaos synchronization of hyperchaotic systems addressed in this paper.

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References

  1. Alligood, K.T., Sauer, T., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer, New York (1997)

    Book  MATH  Google Scholar 

  2. Fujikasa, H., Yamada, T.: Stability theory of synchronized motion in coupled-oscillator systems. Progr. Theoret. Phys. 69, 32–47 (1983)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Pecora, L.M., Carroll, T.L.: Synchronizing chaotic circuits. IEEE Trans. Circ. Sys. 38, 453–456 (1991)

    Article  MATH  Google Scholar 

  5. Lakshmanan, M., Murali, K.: Chaos in Nonlinear Oscillators: Controlling and Synchronization. World Scientific, Singapore (1996)

    Book  MATH  Google Scholar 

  6. Han, S.K., Kerrer, C., Kuramoto, Y.: Dephasing and burstling in coupled neural oscillators. Phys. Rev. Lett. 75, 3190–3193 (1995)

    Article  Google Scholar 

  7. Blasius, B., Huppert, A., Stone, L.: Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399, 354–359 (1999)

    Article  Google Scholar 

  8. Kwok, H.S., Wallace, K., Tang, S., Man, K.F.: Online secure communication system using chaotic map. Internat. J. Bifurcat. Chaos. 14, 285–292 (2004)

    Article  MATH  Google Scholar 

  9. Kocarev, L., Parlitz, U.: General approach for chaos synchronization with applications to communications. Phys. Rev. Lett. 74, 5028–5030 (1995)

    Article  Google Scholar 

  10. Murali, K., Lakshmanan, M.: Secure communication using a compound signal using sampled-data feedback. Applied Math. Mech. 11, 1309–1315 (2003)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Park, J.H., Kwon, O.M.: A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos, Solit. Fract. 17, 709–716 (2003)

    Article  MathSciNet  Google Scholar 

  14. Wu, X., Lü, J.: Parameter identification and backstepping control of uncertain Lü system. Chaos, Solit. Fract. 18, 721–729 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Samuel, B.: Adaptive synchronization between two different chaotic dynamical systems. Adaptive Commun. Nonlinear Sci. Num. Simul. 12, 976–985 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu, Y.G., Zhang, S.C.: Adaptive backstepping synchronization of uncertain chaotic systems. Chaos, Solit. Fract. 27, 1369–1375 (2006)

    Article  Google Scholar 

  17. Park, J.H., Lee, S.M., Kwon, O.M.: Adaptive synchronization of Genesio-Tesi system via a novel feedback control. Physics Lett. A. 371, 263–270 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Park, J.H.: Adaptive control for modified projective synchronization of a four-dimensional chaotic sytem with uncertain parameters. J. Comput. Applied Math. 213, 288–293 (2008)

    Article  MATH  Google Scholar 

  19. Yau, H.T.: Design of adaptive sliding mode controller for chaos synchronization with uncertainties. Chaos, Solit. Fract. 22, 341–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Chen, H.K.: Global chaos synchronization of new chaotic systems via nonlinear control. Chaos, Solit. Fract. 23, 1245–1251 (2005)

    Article  MATH  Google Scholar 

  21. Sundarapandian, V., Suresh, R.: Global chaos synchronization for Rössler and Arneodo chaotic systems. Far East J. Math. Sci. 44, 137–148 (2010)

    MathSciNet  MATH  Google Scholar 

  22. Pang, S., Liu, Y.: A new hyperchaotic system from the Lü system and its control. J. Comput. Applied Math. 235, 2775–2789 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wang, F.Q., Liu, C.X.: Hyperchaos evolved from the Liu chaotic system. Chin. Phys. 15, 963–968 (2006)

    Article  Google Scholar 

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

    Book  MATH  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

  2. School of Electronics and Electrical Engineering, Singhania University, Dist. Jhunjhunu, Rajasthan, 333 515, India

    Karthikeyan Rajagopal

Authors
  1. Sundarapandian Vaidyanathan
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  2. Karthikeyan Rajagopal
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Editor information

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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© 2011 Springer-Verlag Berlin Heidelberg

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Vaidyanathan, S., Rajagopal, K. (2011). Global Chaos Synchronization of Hyperchaotic Pang and Wang 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_9

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  • DOI: https://doi.org/10.1007/978-3-642-24043-0_9

  • 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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