Skip to main content
SpringerLink
Log in

Adaptive multi switching combination synchronization of chaotic systems with unknown parameters

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

Adaptive control method is used to investigate the multi switching combination synchronization (MSCS) between three non identical chaotic systems with fully unknown parameters. In MSCS, the state variables of two drive systems synchronize with different state variables of response system, simultaneously. The Ritikate and Windmi chaotic systems are taken as drive systems and Chen system is taken as response system in the presence of unknown parameters. Some cases of multi switching modified projective synchronization among chaotic systems are obtained as special cases of MSCS. Using Lyapunov stability theory and adaptive control technique, sufficient condition is obtained for attaining the desired theoretical results. Numerical simulations are performed using MATLAB to verify the results.

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

Similar content being viewed by others

References

  1. Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64:821–824

    Article  MathSciNet  MATH  Google Scholar 

  2. Blasius B, Huppert A, Stone L (1999) Complex dynamics and phase synchronization in spatially extended ecological system. Nature 399:354–359

    Article  Google Scholar 

  3. Lakshmanan M, Murali K (1996) Chaos in nonlinear oscillators: controlling and synchronization. World Scientific, Singapore

    Book  MATH  Google Scholar 

  4. Han SK, Kerrer C, Kuramoto Y (1995) D-phasing and bursting in coupled neural oscillators. Phys Rev Lett 75:3190–3193

    Article  Google Scholar 

  5. Lai CW, Chen CK, Liao T, Yan JJ (2008) Adaptive synchronization for nonlinear FitzHugh–Nagumo neurons in external electrical stimulation. Int J Adapt Control Signal Process 22:833–844

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen M, Zhou D, Shang Y (2005) A new observer-based synchronization scheme for private communication. Chaos Solitons Fract 24:1025–1030

    Article  MATH  Google Scholar 

  7. Kwon OM, Park JH, Lee SM (2011) Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn 63:239–252

    Article  MathSciNet  MATH  Google Scholar 

  8. Yao C, Zhao Q, Yu J (2013) Complete synchronization induced by disorder in coupled chaotic lattices. Phys Lett A 377:370–377

    Article  Google Scholar 

  9. Zhu H (2010) Anti-synchronization of two different chaotic systems via optimal control with fully unknown parameters. J Inf Comput Sci 5:011–018

    Google Scholar 

  10. Mahmoud EE (2013) Modified projective phase synchronization of chaotic complex nonlinear systems. Math Comput Simul 89:69–85

    Article  MathSciNet  Google Scholar 

  11. Yu J, Hu C, Jiang H, Teng Z (2012) Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control. Math Comput Simul 82:895–908

    Article  MathSciNet  MATH  Google Scholar 

  12. Odibat ZM (2013) A note on phase synchronization in coupled chaotic fractional order systems. Nonlinear Anal Real World Appl 13:779–789

    Article  MathSciNet  MATH  Google Scholar 

  13. Bowong S, McClintock PVE (2006) Adaptive synchronization between chaotic dynamical systems of different order. Phys Lett A 358:134–141

    Article  MATH  Google Scholar 

  14. Mossa Al-sawalha M, Noorani MSM (2011) Adaptive increasing-order synchronization and anti-synchronization of chaotic systems with uncertain parameters. Chin Phys Lett 28:110507

    Article  Google Scholar 

  15. Srivastava M, Ansari SP, Agrawal SK, Das S, Leung AYT (2014) Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method. Nonlinear Dyn 76:905–914

    Article  MathSciNet  Google Scholar 

  16. Liu X, Chen T, Lu W (2011) Cluster synchronization in uncertain neural networks through adaptive controllers. Differ Equ Dyn Syst 19:47–61

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang CC (2012) Robust synchronization and anti-synchronization of identical \(\phi ^6\) oscillators via adaptive sliding mode control. J Sound Vib 331:501–509

    Article  Google Scholar 

  18. Park JH, Kwon OM (2005) A novel criterion for delayed feedback control of time-delay chaotic systems. Chaos Soliton Fract 23:495–501

    Article  MathSciNet  MATH  Google Scholar 

  19. Vaidyanathan S (2013) Anti-synchronization backstepping control design for Arneodo chaotic system. Int J Bioinform Biosci 3:21–33

    Google Scholar 

  20. Senouci A, Boukabou A (2014) Predictive control and synchronization of chaotic and hyperchaotic systems based on a T-S fuzzy model. Math Comput Simul 105:62–78

    Article  MathSciNet  Google Scholar 

  21. Luo RZ, Wang YL, Deng SC (2011) Combination synchronization of three classic chaotic systems using active backstepping design. Chaos 21:043114

    Article  MATH  Google Scholar 

  22. Runzi L, Yinglan W (2013) Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication. Chaos 22:023109

    Article  MathSciNet  MATH  Google Scholar 

  23. Wu Z, Fu X (2013) Combination synchronization of three different order nonlinear systems using active backstepping design. Nonlinear Dyn 73:1863–1872

    Article  MathSciNet  MATH  Google Scholar 

  24. Wu A (2014) Hyperchaos synchronization of memristor oscillator system via combination scheme. Adv Differ Equ 2014(1):86–96

    Article  MathSciNet  Google Scholar 

  25. Ucar A, Lonngren KE, Bai EW (2008) Multi-switching synchronization of chaotic systems with active controllers. Chaos Solitons Fract 38:254–262

    Article  Google Scholar 

  26. Yu F, Wang CH, Wan QZ, Hu Y (2013) Complete switched modified function projective synchronization of a five-term chaotic system with uncertain parameters and disturbances. Pramana 80:223–235

  27. Wang XY, Sun P (2011) Multi-switching synchronization of chaotic system with adaptive controllers and unknown parameters. Nonlinear Dyn 63:599–609

    Article  MathSciNet  Google Scholar 

  28. Khan A, Khattar D, Prajapati N (2017) Multiswitching combination-combination synchronization of chaotic systems. Pramana 88:47

    Article  Google Scholar 

  29. Khan A, Khattar D, Prajapati N (2017) Reduced order multi switching hybrid synchronization of chaotic systems. J Math Comput Sci 7:414–429

    Google Scholar 

  30. Vincent UE, Saseyi AO, McClintock PVE (2015) Multi-switching combination synchronization of chaotic systems. Nonlinear Dyn 80:845–854

    Article  MathSciNet  MATH  Google Scholar 

  31. Feki M (2009) Sliding mode control and synchronization of chaotic systems with parametric uncertainties. Chaos Solitons Fract 41:1390–1400

    Article  MathSciNet  MATH  Google Scholar 

  32. Sun J, Shen Y, Wang X, Chen J (2014) Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control. Nonlinear Dyn 76:383–397

    Article  MathSciNet  MATH  Google Scholar 

  33. Hamid HPA, Ali KK, Jafar FAS, Reza GM, Sadegh M, Moosa Y (2015) Appl Sci Rep 9:80–86

    Google Scholar 

  34. Zhao J, Zhang K (2010) Adaptive function Q-S synchronization of chaotic systems with unknown parameters. Int J Adapt Control Sign Process 24:675–686

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank the anonymous reviewers for the valuable comments and suggestions leading to improvement of this paper. The work of the third author is supported by the Senior Research Fellowship of Council of Scientific and Industrial Research, India(Grant No. 09/045(1319)/2014-EMR-I).

Author information

Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, Delhi, India

    Ayub Khan

  2. Department of Mathematics, Kirorimal College, University of Delhi, Delhi, India

    Dinesh Khattar

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

    Nitish Prajapati

Authors
  1. Ayub Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dinesh Khattar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nitish Prajapati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nitish Prajapati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, A., Khattar, D. & Prajapati, N. Adaptive multi switching combination synchronization of chaotic systems with unknown parameters. Int. J. Dynam. Control 6, 621–629 (2018). https://doi.org/10.1007/s40435-017-0320-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-017-0320-z

Keywords

Search

Navigation