Skip to main content
SpringerLink
Log in

Multiswitching compound–compound synchronisation of six chaotic systems

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, a novel synchronisation scheme involving six chaotic systems is proposed. The proposed scheme is named as ‘compound–compound synchronisation’. Instead of using a scaling system in compound synchronisation, a compound scaling signal is applied to the proposed scheme. The phenomenon of multiswitching synchronisation and the proposed scheme are combined together. Appropriate controllers are designed by employing nonlinear control method and Lyapunov stability theory to achieve asymptotically stable synchronisation states. An example of identical Chen systems is presented to demonstrate the proposed methodology. The proposed scheme is very different and complex in comparison with the previous schemes, as this scheme is first of its kind having five drive systems and one response system. Computational results are presented to justify the theoretical analysis. Numerical results and theoretical studies converge to the same conclusions.

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

Similar content being viewed by others

References

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

    Article  ADS  MathSciNet  Google Scholar 

  2. S O Kareem, K S Ojo and A N Njah, Pramana – J. Phys. 79, 71 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. X Jian, Int. J. Phys. Sci. 6, 2478 (2011)

    Google Scholar 

  5. W He and J Cao, Chaos 19, 013118 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. M A Khan, M Nag and S Poria, Pramana – J. Phys. 89: 19 (2017)

    Article  ADS  Google Scholar 

  7. P P Singh, J P Singh and B K Roy, Chaos Solitons Fractals 69, 31 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  8. G Feng and J Cao, Adv. Differ. Equ. 2013, 24 (2013)

    Article  Google Scholar 

  9. R Luo, H Su and Y Zeng, Chin. J. Phys. 55, 342 (2017)

    Article  Google Scholar 

  10. W Jawaada, M S Noorani and M M Al-Sawalha, Chin. Phys. Lett. 29, 120505 (2012)

    Article  Google Scholar 

  11. K S Sudheer and M Sabir, Pramana – J. Phys. 88: 40 (2017)

    Article  ADS  Google Scholar 

  12. L Runzi, W Yinglan and D Shucheng, Chaos 21, 043114 (2011)

    Article  ADS  Google Scholar 

  13. J Sun, Y Shen, G Zhang, C Xu and G Cui, Nonlinear Dyn. 73, 1211 (2013)

    Article  Google Scholar 

  14. Z Wu and X Fu, Nonlinear Dyn. 73, 1863 (2013)

    Article  Google Scholar 

  15. A Wu and J Zhang, Adv. Differ. Equ. 2014, 100 (2014)

    Article  Google Scholar 

  16. J Sun, Y Wang, Y Wang, G Cui and Y Shen, Optik 127, 4136 (2016)

    Article  ADS  Google Scholar 

  17. B Zhang and F Deng, Nonlinear Dyn. 77 , 1519 (2014)

    Article  Google Scholar 

  18. L Runzi and W Yinglan, Chaos 22, 023109 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  19. J Sun, Y Shen, Q Yin and C Xu, Chaos 23, 013140 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  20. A Ucar, K E Lonngren and E W Bai, Chaos Solitons Fractals 38, 254 (2008)

    Article  ADS  Google Scholar 

  21. A A Ajayi, S K Ojo, E U Vincent and N A Njah, J. Nonlinear Dyn. 2014, 918586 (2014)

    Google Scholar 

  22. X Wang and P Sun, Nonlinear Dyn. 63, 599 (2011)

    Article  Google Scholar 

  23. U E Vincent, A O Saseyi and P V E McClintock, Nonlinear Dyn. 80, 845 (2015)

    Article  Google Scholar 

  24. S Zheng, Optik 127, 10247 (2016)

    Article  ADS  Google Scholar 

  25. A Khan, D Khattar and N Prajapati, Pramana – J. Phys. 88: 47 (2017)

    Article  ADS  Google Scholar 

  26. A Khan, M Budhraja and A Ibraheem, Int. J. Dyn. Control 6, 1126 (2018)

    Article  MathSciNet  Google Scholar 

  27. G Chen and T Ueta, Int. J. Bifurc. Chaos 9, 1465 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110 025, India

    Ayub Khan

  2. Department of Mathematics, Shivaji College, New Delhi, 110 027, India

    Mridula Budhraja

  3. Department of Mathematics, University of Delhi, Delhi, 110 007, India

    Aysha Ibraheem

Authors
  1. Ayub Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mridula Budhraja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aysha Ibraheem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aysha Ibraheem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, A., Budhraja, M. & Ibraheem, A. Multiswitching compound–compound synchronisation of six chaotic systems. Pramana - J Phys 91, 73 (2018). https://doi.org/10.1007/s12043-018-1647-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1647-5

Keywords

PACS Nos

Search

Navigation