Skip to main content
SpringerLink
Log in

Dynamics of fractional-ordered Chen system with delay

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In the present paper the effect of delay on chaos in fractional-order Chen system is investigated. It is observed that inclusion of delay changes chaotic behaviour to limit cycles or stable systems.

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

Similar content being viewed by others

References

  1. H H Sun, A A Abdelwahad and B Onaral, IEEE Trans. Automat. Control 29, 441 (1984)

    Article  MATH  Google Scholar 

  2. W R Schneider and W Wyss, J. Math. Phys. 30(1), 134 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. F Mainardi, Y Luchko and G Pagnini, Fractional Calculus and Appl. Anal. 4(2), 153 (2001)

    MathSciNet  MATH  Google Scholar 

  4. V Daftardar-Gejji and H Jafari, Australian J. Math. Anal. Appl. 3, 1 (2006)

    MathSciNet  Google Scholar 

  5. V Daftardar-Gejji and S Bhalekar, Appl. Math. Comput. 202, 113 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. M Caputo and F Mainardi, Pure Appl. Geophys. 91, 134 (1971)

    Article  ADS  Google Scholar 

  7. T J Anastasio, Biol. Cybernet. 72, 69 (1994)

    Article  Google Scholar 

  8. R L Magin, Fractional calculus in bioengineering (Begell House Publishers, USA, 2006)

    Google Scholar 

  9. A A Stanislavsky, Phys. Rev. E70, 051103 (2004)

    ADS  Google Scholar 

  10. M S Tavazoei, M Haeri and N Nazari, Signal Process. 88, 2971 (2008)

    Article  MATH  Google Scholar 

  11. E N Lorenz, J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  12. K T Alligood, T D Sauer and J A Yorke, Chaos: An introduction to dynamical systems (Springer, New York, 2008)

    Google Scholar 

  13. I Grigorenko and E Grigorenko, Phys. Rev. Lett. 91, 034101 (2003)

    Article  ADS  Google Scholar 

  14. V Daftardar-Gejji and S Bhalekar, Comput. Math. Appl. 59, 1117 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. O E Rössler, Phys. Lett. A57(5), 397 (1976)

    ADS  Google Scholar 

  16. J C Sprott, Phys. Lett. A228, 271 (1997)

    MathSciNet  ADS  Google Scholar 

  17. G Chen and T Ueta, Int. J. Bifurcat. Chaos 9, 1465 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  18. Z T Hou, N Kang, X X Kong, G R Chen and G J Yan, Int. J. Bifurcat. Chaos 20, 557 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. A Vanêcek and S Ĉelikovskÿ, Control systems: From linear analysis to synthesis of chaos (Prentice-Hall, London, 1996)

    MATH  Google Scholar 

  20. J G Lü, Phys. Lett. A354(4), 305 (2006)

    ADS  Google Scholar 

  21. M C Mackey and L Glass, Science 197, 287 (1977)

    Article  ADS  Google Scholar 

  22. E Fridman, L Fridman and E Shustin, J. Dyn. Sys. Meas. Control 122, 732 (2000)

    Article  Google Scholar 

  23. L C Davis, Physica A319, 557 (2002)

    ADS  Google Scholar 

  24. Y Kuang, Delay differential equations with applications in population biology (Academic Press, Boston, San Diego, New York, 1993)

    Google Scholar 

  25. I Epstein and Y Luo, J. Chem. Phys. 95, 244 (1991)

    Article  ADS  Google Scholar 

  26. J K Hale and S M V Lunel, Introduction to functional differential equations, applied mathematical sciences (Springer-Verlag, Berlin, 1993)

    Google Scholar 

  27. C Li and G Peng, Chaos, Solitons and Fractals 22, 443 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. I Podlubny, Fractional differential equations (Academic Press, San Diego, 1999)

    MATH  Google Scholar 

  29. S G Samko, A A Kilbas and O I Marichev, Fractional integrals and derivatives: Theory and applications (Gordon and Breach, Yverdon, 1993)

    MATH  Google Scholar 

  30. K Diethelm, Elec. Trans. Numer. Anal. 5, 1 (1997)

    MathSciNet  MATH  Google Scholar 

  31. K Diethelm, N J Ford and A D Freed, Nonlin. Dyn. 29, 3 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. S Bhalekar and V Daftardar-Gejji, J. Fractional Calculus and Applications 1(5), 1 (2011)

    MathSciNet  Google Scholar 

  33. T Ueta and G Chen, Int. J. Bifurcat. Chaos 10(8), 1917 (2000)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pune, Ganeshkhind, Pune, 411 007, India

    VARSHA DAFTARDAR-GEJJI

  2. Department of Mathematics, Shivaji University, Kolhapur, 416 004, India

    SACHIN BHALEKAR

  3. PG Department of Physics, Rastrasant Tukdoji Maharaj Nagpur University, Nagpur, 440 033, India

    PRASHANT GADE

Authors
  1. VARSHA DAFTARDAR-GEJJI
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. SACHIN BHALEKAR
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. PRASHANT GADE
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to VARSHA DAFTARDAR-GEJJI.

Rights and permissions

Reprints and permissions

About this article

Cite this article

DAFTARDAR-GEJJI, V., BHALEKAR, S. & GADE, P. Dynamics of fractional-ordered Chen system with delay. Pramana - J Phys 79, 61–69 (2012). https://doi.org/10.1007/s12043-012-0291-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-012-0291-8

Keywords

PACS Nos

Search

Navigation