Skip to main content
SpringerLink
Log in

Modified projective synchronization of chaotic dissipative gyroscope systems via backstepping control

  • Original paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

This paper proposes the modified projective synchronization for heavy symmetric dissipative gyroscope systems via backstepping control. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. Using the backstepping control technique, control laws are established which guarantees the hybrid projective synchronization including synchronization, anti-synchronization and projective synchronization. By Lyapunov stability theory, control laws are proposed to ensure the stability of the controlled closed-loop. Numerical simulations are presented to verify the proposed synchronization approach. This paper demonstrates that synchronization and anti-synchronization can coexist in dissipative gyroscope systems via nonlinear control.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. G Chen Controlling Chaos and Bifurcations in Engineering Systems (Boca Raton: CRC Press) (1999).

    Google Scholar 

  2. L M Pecora and T L Carroll Phys. Rev. Lett. 64 821 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  3. J Z Yang, G Hu and J H Xiao Phys. Rev. Lett. 80 496 (1998)

    Article  ADS  Google Scholar 

  4. E M Shahverdiev Phys. Rev. E. 70 067202 (2004)

    Article  ADS  Google Scholar 

  5. J F Xu, L Q Min, and G R Chen Chin Phys. Lett. 21 1445 (2004)

    Article  ADS  Google Scholar 

  6. N F Rulkov, M M Sushchik and L S Tsimring Phys. Rev. E. 51 980 (1995)

    Article  ADS  Google Scholar 

  7. M G Rosenblutn, A S Pikovsky and J Kurths Phys. Rev. Lett. 76 1804 (1996)

    Article  ADS  Google Scholar 

  8. L Y Cao and Y C Lai Phys. Rev. E. 58 382 (1998)

    Article  ADS  Google Scholar 

  9. R Mainieri and J Rehacek Phys. Rev. Lett. 82 3042 (1999)

    Article  ADS  Google Scholar 

  10. G L Wen and D L Xu Chaos Solitons Fractals 26 71 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. G L Wen and D L Xu Phys. Lett. A. 333 420 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. J Yan and C Li Chaos Solitons Fractals 26 1119 (2005)

    Article  ADS  MATH  Google Scholar 

  13. J P Yan and C P Li J. Shanghai Univ. 10 299 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. F Farivar, M A Shoorehdeli, M A Nekoui and M Teshnehlab Chaos Solitons Fractals 42 826 (2009)

    Article  ADS  MATH  Google Scholar 

  15. G H Li Chaos Solitons Fractals 32 1786 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. S Roy, S Sil and A Chakravarti Indian J. Phys. 84 301 (2010)

    Article  ADS  Google Scholar 

  17. K Rai Dastidar Indian J. Phys. 84 947 (2010)

    Article  Google Scholar 

  18. B Dahiya, D Munjal and V Prasad Indian J. Phys. 85 1721 (2011)

    Article  ADS  Google Scholar 

  19. S Mitra, M M Hossain, B Roy and P N Ghosh Indian J. Phys. 84 969 (2010)

  20. G Mandal and T Ganguly Indian J. Phys. 32 1299 (2011)

    Google Scholar 

  21. A Goswami, T Bezboruah and K C Sarma Indian J. Phys. 84 71 (2010)

    Article  ADS  Google Scholar 

  22. H Khalil Nonlinear Sytems (3rd ed.) (Upper Saddle River: Prentice-Hall) (2002)

  23. C F Hsu, C M Lin and T T Lee IEEE Trans. Neural Netw. 17 1175 (2006)

    Article  Google Scholar 

  24. M T Yassen Chaos Solitons Fractals 27 537 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. F Farivar, M A Shoorehdeli, M A Nekoui and M Teshnehlab J. Appl. Sci. 9 284 (2009)

    Google Scholar 

  26. R B Leipnik and T A Newton Phys. Lett. A. 86 63 (1981)

    Article  MathSciNet  ADS  Google Scholar 

  27. Z M Ge, C L Hsiao, Y S Chen and C M Chang Int. J. Nonlinear. Sci. Numer. Simul. 8 89 (2007)

    Article  Google Scholar 

  28. H K Chen and Z M Ge Chaos Solitons and Fractals 24 125 (2005)

    MathSciNet  ADS  MATH  Google Scholar 

  29. H T Yau J. Nonlinear Anal. Real World Appl. 9 2253 (2008)

    Article  MATH  Google Scholar 

  30. F Farivar, M A Shoorehdeli, M A Nekoui and M Teshnehlab IEEE/ASME Inter. Conf. Adv. Intelligent Mechatronics p 1365 (2009)

Download references

Author information

Authors and Affiliations

  1. Department of Mechatronics Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    F. Farivar

  2. Department of Control Engineering, Faculty of Electrical Engineering, K N Toosi University of Technology, Tehran, Iran

    M. A. Nekoui & M. Teshnehlab

  3. Department of Mechatronics Engineering, Faculty of Electrical Engineering, K N Toosi University of Technology, Tehran, Iran

    M. A. Shoorehdeli

Authors
  1. F. Farivar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Nekoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Shoorehdeli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Teshnehlab
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Farivar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Farivar, F., Nekoui, M.A., Shoorehdeli, M.A. et al. Modified projective synchronization of chaotic dissipative gyroscope systems via backstepping control. Indian J Phys 86, 901–906 (2012). https://doi.org/10.1007/s12648-012-0139-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-012-0139-6

Keywords

PACS Nos.

Search

Navigation