Skip to main content

Synchronization of Fractional-Order Chaotic System with Application to Communication

  • Conference paper
  • First Online:
Informatics in Control, Automation and Robotics

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 132))

Abstract

This paper studied the synchronization of fractional-order chaotic system based on the theory of fractional calculus, and the synchronization between the two identical fractional-order Chen systems is realized after 0.6s by using the active control, and the simulation results verify the effectiveness of the examined method. Furthermore, the control scheme can be used in secure communication via the technology of chaotic masking. Numerical simulations coincide with the theoretical analysis.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Podlubny, I.: Fractional differential equations. Academic Press, New York (1999)

    MATH  Google Scholar 

  2. Bagley, R.L., Calico, R.A.: Fractional order state equations for the control of viscoelastically damped structures. Journal of Guidance, Control, and Dynamics 14, 304–311 (1991)

    Article  Google Scholar 

  3. Koeller, R.C.: Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mesh. 51, 299–307 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ichise, M., Nagayanagi, Y., Kojima, T.: An analog simulation of noninteger order transfer functions for analysis of electrode process. J. Electroanal. Chem. 33, 253–265 (1971)

    Google Scholar 

  5. Heaviside, O.: Electromagnetic theory, New York,Chelsea (1971)

    Google Scholar 

  6. Li, C., Chen, G.: Chaos and hyperchaos in the fractional order Rŏssler equations. Physica A 41, 55–61 (2004)

    Article  Google Scholar 

  7. Li, C.G., Liao, X.F., Yu, J.B.: Synchronization of fractional order chaotic systems. Phys. Rev. E. 68, 1–3 (2003)

    Google Scholar 

  8. Wu, X., Lu, Y.: Generalized projective synchronization of the fractional-order Chen hyperchaotic system. Nonlinear Dyn. 57, 25–35 (2009)

    Article  MATH  Google Scholar 

  9. Yan, J.P., Li, C.P.: On chaos synchronization of fractional differential equations. Chaos Solitons & Fractals 32, 725–735 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wang, Z., Zhang, H., Li, Y., et al.: A New Method on Synchronization of Fractional-Order.Chaotic Systems. In: Proceedings of 2010 Chinese Control and Decision Conference, vol. 07, pp. 3357–3362 (2010)

    Google Scholar 

  11. Ruan, H., Zhai, T., Yaz, E.E.: A chaotic secure chaotic communication scheme with extended Kalman filter based parameter estimation. In: Proceeding of IEEE Conference on Control Applications, vol. 26, pp. 404–408 (2003)

    Google Scholar 

  12. Chen, M., Zhou, D., Shang, Y.: A sliding mode adaptive observer chaotic communication scheme. Chaos, Solitions & Fractals 253, 573–578 (2005)

    Article  MathSciNet  Google Scholar 

  13. Huang, C.-F., Hung, M.-L., et al.: Chaos-based Secure Communication via control. World Academy of Science 119, 650–653 (2010)

    Google Scholar 

  14. Kiani-B, A., Fallahi, K., Pariz, N., Leung, H.: A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Commun. Nonlinear Sci. Numer. Simul. 14, 863–879 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Deng, Y.-S., Qin, K.-Y.: Fractional order Liu-system synchronization and its application in multimedia security. In: ICCCAS, vol. 23, pp. 769–772 (2010)

    Google Scholar 

  16. Oppenheim, A.V., Womell, C.W., Isabelle, S.H.: Signal processing in the context of chaotic signals. In: IEEE Int. Conf. ASSP, vol. 23, pp. 117–120 (1992)

    Google Scholar 

  17. Hartley, T.T., Lorenzo, C.F., Qammer, H.K.: Chaos in a fractional order Chua’s system. IEEE Trans. CAS-I 42, 485–490 (1995)

    Article  Google Scholar 

  18. Agiza, H.N., Yassen, M.T.: Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys. Lett. A 278, 191–197 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wen, T., Fengling, J., Xianqun, L., Jian Xun, L., Feng, W. (2011). Synchronization of Fractional-Order Chaotic System with Application to Communication. In: Tan, H. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25899-2_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25899-2_31

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25898-5

  • Online ISBN: 978-3-642-25899-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics