Skip to main content

Analysis and Synchronization of the Hyperchaotic Yujun Systems via Sliding Mode Control

  • Conference paper

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 176))

Abstract

In this paper, we deploy sliding mode control (SMC) to derive new results for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). The synchronization results derived in this paper are established using the Lyapunov stability theory. Numerical simulations have been provided to illustrate the sliding mode control results derived in this paper for the complete synchronization of identical hyperchaotic Yujun systems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. 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 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  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. Ho, M.C., Hung, Y.C.: Synchronization of two different chaotic systems using generalized active network. Phys. Lett. A 301, 421–428 (2002)

    Article  MathSciNet  Google Scholar 

  11. Huang, L., Feng, R., Wang, M.: Synchronization of chaotic systems via nonlinear control. Phys. Lett. A 320, 271–275 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  13. Sundarapandian, V.: Global chaos synchronization of Shimizu-Morioka and Liu-Chen chaotic systems by active nonlinear control. Internat. J. Advances in Science and Technology 2(4), 11–20 (2011)

    Google Scholar 

  14. Chen, S.H., Lü, J.: Synchronization of an uncertain unified system via adaptive control. Chaos, Solit. Frac. 14, 643–647 (2002)

    Article  MATH  Google Scholar 

  15. Lu, J., Han, X., Lü, J.: Adaptive feedback synchronization of a unified chaotic system. Phys. Lett. A 329, 327–333 (2004)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  18. 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 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhao, J., Lu, J.: Using sampled-data feedback control and linear feedback synchronization in a new hyperchaotic system. Chaos, Solit. Fract. 35, 376–382 (2008)

    Article  Google Scholar 

  23. Slotine, J.E., Sastry, S.S.: Tracking control of nonlinear systems using sliding surface with application to robotic manipulators. Internat. J. Control 38, 465–492 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  24. Utkin, V.I.: Sliding mode control design principles and applications to electric drives. IEEE Trans. Industrial Electr. 40, 23–36 (1993)

    Article  Google Scholar 

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

    Google Scholar 

  26. Yujun, N., Xingyuan, W., Mingjun, W., Huaguang, Z.: A new hyperchaotic system and its circuit implementation. Commun. Nonlinear Sci. Numer. Simulat. 15, 3518–3524 (2010)

    Article  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sundarapandian Vaidyanathan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vaidyanathan, S. (2012). Analysis and Synchronization of the Hyperchaotic Yujun Systems via Sliding Mode Control. In: Meghanathan, N., Nagamalai, D., Chaki, N. (eds) Advances in Computing and Information Technology. Advances in Intelligent Systems and Computing, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31513-8_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31513-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31512-1

  • Online ISBN: 978-3-642-31513-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics