Skip to main content
SpringerLink
Log in

Control of partial synchronization in chaotic oscillators

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

A design of coupling is proposed to control partial synchronization in two chaotic oscillators in a driver–response mode. A control of synchrony between one response variables is made possible (a transition from a complete synchronization to antisynchronization via amplitude death and vice versa without loss of synchrony) keeping the other pairs of variables undisturbed in their pre-desired states of coherence. Further, one of the response variables can be controlled so as to follow the dynamics of an external signal (periodic or chaotic) while keeping the coherent status of other variables unchanged. The stability of synchronization is established using the Hurwitz matrix criterion. Numerical example of an ecological foodweb model is presented. The control scheme is demonstrated in an electronic circuit of the Sprott system.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Similar content being viewed by others

References

  1. V N Belykh, G V Osipov, N Kucklander, B Blasius and J Kurths, Physica D 200, 81 (2005)

  2. M G Rosenblum and A S Pikovsky, Phys. Rev. Lett. 92, 114102 (2004)

  3. P A Popovych and P A Tass, Phys. Rev. E 82, 026204 (2010)

  4. O V Popovych, C Hauptmann and P A Tass, Phys. Rev. Lett. 94, 164102 (2005)

  5. I Z Kiss, C G Rusin, H Kori and J L Hudson, Science 316(5853), 1886 (1995)

  6. J-R Kim, D Shin, S H Jung, P-H Harrison and K-H Cho, J. Cell Sci. 123(4), 537 (2010)

  7. A Prasad, M Dhamala, B M Adhikari and R Ramaswamy, Phys. Rev. E 82, 027201 (2010)

  8. K Pyragas and T Pyragine, Phys. Rev. E 78, 046217 (2008)

  9. C Hens, R Banerjee, U Feudel and S K Dana, Phys. Rev. E 85, 025200(R) (2012)

  10. E A Jackson and I Grosu, Physica D 85, 1 (1995) I Grosu, Phys. Rev. E 56, 3709 (1997); ibid, Int. J. Bifurcat. Chaos Appl. Sci. Eng. 17, 3519 (2007)

  11. I Grosu, E Padmanaban, P K Roy and S K Dana, Phys. Rev. Lett. 100, 234102 (2008)

  12. I Grosu, R Banerjee, P K Roy and S K Dana, Phys. Rev. E 80, 016212 (2009)

  13. P K Roy, C Hens, I Grosu and S K Dana, Chaos 21, 013106 (2011)

  14. K S Sudheer and M Sabir, Pramana – J. Phys. 73(4), 781 (2009)

  15. C Sun, W Sun and J Kurths, Phys. Rev. E 76, 046204 (2007) R Banerjee, I Grosu and S K Dana, Proc. Complex (LNICST 4), Computer Science Series (Springer, New York, 2009), Pt. I, pp. 1072–1082

  16. E Padmanaban, C Hens and S K Dana, Chaos 21, 013110 (2011)

  17. Richard C Dorf and Robert H Bishop, Modern control systems (Prentice Hall, 2001) A Hurwitz, On the conditions under which an equation has only roots with negative real parts, Selected Papers on Mathematical Trends in Control Theory (1964)

  18. L Janagal and P Parmananda, Phys. Rev. E 86, 056213 (2012)

  19. A Pikovsky, M Rosenblum and J Kurths, Synchronization: A universal concept in nonlinear sciences (Cambridge University Press, Cambridge, England, 2001)

  20. L Pecora and T Carroll, Phys. Rev. Lett. 64, 821 (1990)

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

  22. M G Rosenblum, A S Pikovsky and J Kurths, Phys. Rev. Lett. 78, 4193 (1997)

  23. L-Y Cao and Y-C Lai, Phys. Rev. E 58, 38 (1998) V Astakov, A Shabun and V Anischencko, Int. J. Bifurcat. Chaos Appl. Sci. Engg. 10, 849 (2000) W Liu et al, Phys. Rev. E 73, 057203 (2006) C-M Kim et al, Phys. Lett. A 320, 39 (2003) V Belykh, I Belykh and M Hasler, Phys. Rev. E 62, 6332(2000) S K Dana, B Blasius and J Kurths, Chaos 16, 023111 (2006)

  24. S Zambrano, M A F Sanjuán and J A Yorke, Phys. Rev. E 77, 055201(R) (2008)

  25. R Capeáns, J Sabuco and M A F Sanjuán, Ecological Complexity 19, 1 (2014)

  26. L M Pecora, F Sorrentino, A M Hagerstrom, T E Murphy and R Roy, Nature Commun. 5, 4079 (2014), DOI:10.1038/ncomms5079

  27. Y Kuramoto and D Battogtokh, Nonlin. Phen. Complex Sys. 5, 380 (2002)

  28. D M Abrams and S H Strogatz, Phys. Rev. Lett. 93, 174102 (2004)

  29. S Boccaletti, J Kurths, G Osipov, D L Valladares and C S Zhou, Phys. Rep. 366, 1 (2002)

  30. E Padmanaban, S Boccaletti and S K Dana, Phys. Rev. E (submitted)

  31. E Ullner, A Zaikin, E I Volkov and J García-Ojavlo, Phys. Rev. Lett. 99, 148103 (2007)

  32. E Ullner, A Koseska, J Kurths, E I Volkov, H Kantz and J García-Ojavlo, Phys. Rev. E 78, 031904 (2008)

  33. E Padmanaban, R Banerjee and S K Dana, Int. J. Bifurcat. Chaos 22(7) , 1250177 (2012)

  34. D V Ramana Reddy, A Sen and G L Johnston, Phys. Rev. Lett. 80, 5109 (1998) R Dodla, A Sen and G L Johnston, Phys. Rev. E 69, 056217 (2004)

  35. A Koseska, E Volkov and J Kurths, Chaos 20, 023132 (2010) K Bar-Eli, J. Phys. Chem. 88, 3616 (1985)

  36. A Koseska, E Volkov and J Kurths, Phys. Rep. 531(4), 173 (2013)

  37. C R Hens, P Pal, S K Bhowmick, P K Roy, A Sen and S K Dana, Phys. Rev. E 89, 032901 (2014)

  38. B Blasius, A Huppert and L Stone, Nature 399, 354 (1999)

  39. R E Amritkar and G Rangarajan, Phys. Rev. Lett. 96, 258102 (2006)

  40. J C Sprott, Phys. Rev. E 50, R647 (1994)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Technology and Management, Shillong, 793 003, India

    R BANERJEE

  2. Central Instrumentation Division, CSIR-Indian Institute of Chemical Biology, Kolkata, 700 032, India

    E PADMANABAN & S K DANA

Authors
  1. R BANERJEE
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E PADMANABAN
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S K DANA
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S K DANA.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

BANERJEE, R., PADMANABAN, E. & DANA, S.K. Control of partial synchronization in chaotic oscillators. Pramana - J Phys 84, 203–215 (2015). https://doi.org/10.1007/s12043-014-0927-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-014-0927-y

Keywords

PACS Nos

Search

Navigation