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Hybrid Synchronization of Hyperchaotic Qi and Lü Systems by Nonlinear Control

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Advances in Computer Science and Information Technology (CCSIT 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 131))

Abstract

This paper investigates the hybrid synchronization of identical hyperbolic Qi systems and hybrid synchronization of hyperchaotic Qi and Lü systems. The hyperchaotic Qi system (2008) and hyperchaotic Lü system (2006) are important models of hyperchaotic systems. Hybrid synchronization of the hyperchaotic systems is achieved through synchronization of two pairs of states and anti-synchronization of the other two pairs of states of the two hyperchaotic systems. Nonlinear control is the method used for the hybrid synchronization of identical hyperbolic Qi systems and hybrid synchronization of hyperchaotic Qi and Lü systems. Since the Lyapunov exponents are not required for these calculations, this method is effective and convenient to achieve hybrid synchronization of the two hyperchaotic systems. Numerical simulations are shown to verify the results.

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solit. Fract. 18, 141–148 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Murali, K., Lakshmanan, M.: Secure communication using a compound signal from generalized synchronizable chaotic systems. Phys. Rev. Lett. A 241, 303–310 (1998)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. 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  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  13. 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 

  14. Ge, Z.M., Chen, C.C.: Phase synchronization of coupled chaotic multiple time scales systems. Chaos, Solit. Fract. 20, 639–647 (2004)

    Article  MATH  Google Scholar 

  15. Wang, Y.W., Guan, Z.H.: Generalized synchronization of continuous chaotic systems. Chaos, Solit. Fract. 27, 97–101 (2006)

    Article  MATH  Google Scholar 

  16. Zhang, X., Zhu, H.: Anti-synchronization of two different hyperchaotic systems via active and adaptive control. Inter. J. Nonlinear Science 6, 216–223 (2008)

    MathSciNet  MATH  Google Scholar 

  17. Chiang, T., Lin, J., Liao, T., Yan, J.: Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity. Nonlinear Anal. 68, 2629–2637 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Qiang, J.: Projective synchronization of a new hyperchaotic Lorenz system. Phys. Lett. A. 370, 40–45 (2007)

    Article  MATH  Google Scholar 

  19. Jian-Ping, Y., Chang-Pin, L.: Generalized projective synchronization for the chaotic Lorenz system and the chaotic Chen system. J. Shanghai Univ. 10, 299–304 (2006)

    Article  MathSciNet  Google Scholar 

  20. Li, R.H., Xu, W., Li, S.: Adaptive generalized projective synchronization in different chaotic systems based on parameter identification. Phys. Lett. A. 367, 199–206 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, R.-h.: A special full-state hybrid projective synchronization in symmetrical chaotic systems. Applied Math. Comput. 200, 321–329, (2008)

    MathSciNet  MATH  Google Scholar 

  22. Qi, G., Wyk, M.A., Wyk, B.J., Chen, G.: On a new hyperchaotic system. Phys. Lett. A 372, 124–136 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chen, A., Lü, J., Lu, J., Yu, S.: Generating hyperchaotic Lü attractor via state feedback control. Physica A 364, 103–110 (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. Department of Mathematics, Vel Tech Dr. RR & Dr. SR Technical University, Avadi-Alamathi Road, Avadi, Chennai, 600 062, India

    Sundarapandian Vaidyanathan & Suresh Rasappan

Authors
  1. Sundarapandian Vaidyanathan
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  2. Suresh Rasappan
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Editor information

Editors and Affiliations

  1. Jackson State University, 39217, Jackson, MS, USA

    Natarajan Meghanathan

  2. Deptt. of Electronics and Computer Engg., Indian Institute of Technology, Roorkee, India

    Brajesh Kumar Kaushik

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

    Dhinaharan Nagamalai

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© 2011 Springer-Verlag Berlin Heidelberg

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Vaidyanathan, S., Rasappan, S. (2011). Hybrid Synchronization of Hyperchaotic Qi and Lü Systems by Nonlinear Control. In: Meghanathan, N., Kaushik, B.K., Nagamalai, D. (eds) Advances in Computer Science and Information Technology. CCSIT 2011. Communications in Computer and Information Science, vol 131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17857-3_58

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  • DOI: https://doi.org/10.1007/978-3-642-17857-3_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17856-6

  • Online ISBN: 978-3-642-17857-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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