Skip to main content
SpringerLink
Log in

Effects of depth potential on the dynamics of Duffing system and chaos control: numerical and electronic implementation

  • Review Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

Numerical and experimental results concerning the control of chaos in the double-well Duffing system with one external force are presented in this paper. Lyapunov exponent is used as the identifier of chaos in the nonlinear system. As the expression of the potential function depends on the damping coefficient, it is found that the depth of the potential well increases with damping. Thus, this paper presents a physical insight into control damping (or coefficient of damping of a system) to quench, and also to prevent chaotic situations, which are considered disturbances and are harmful for operations. It is found that when the depth of the double-well potential increases, it becomes more difficult for the state to switch from one equilibrium to other, and thus, the chaos is suppressed. The new feedback control method based on damping coefficient and Lyapunov exponent is proposed. The experimental investigation using electronic components shows that the results obtained are similar to those observed from numerical investigation.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. P Bala, T S Gill and A S Bains India J. Phys. 91 1625 (2017)

    Article  ADS  Google Scholar 

  2. S Ghosh and A Muley India. J. Phys. 92 121 (2018)

    Article  ADS  Google Scholar 

  3. Y G Zheng and Z H Wang Nonlinear Dyn. 57 125 (2009)

    Article  Google Scholar 

  4. H Simo and P Woafo Optik 127 1 (2016)

    Article  Google Scholar 

  5. L T Abobda and P Woafo Eur. Phys. J. 223 2885 (2014)

    Google Scholar 

  6. B Hu, Z Liandong and Y Jingjing J. Mech. Sci. Technol. 30 5183 (2016)

    Article  Google Scholar 

  7. Y S Kondji, G Fautso Kuiate and P Woafo Phys. Scr. 81 015010 (2010)

    Article  ADS  Google Scholar 

  8. Z Meng, D Yang, H Zhou and B P Wang Struct. Multidisc. Optim. 57 91 (2018)

    Article  Google Scholar 

  9. H Simo and P Woafo Int. J. Bifurcat. Chaos 22 1250003 (2012)

    Article  Google Scholar 

  10. D O Tcheutchoua Fossi and P Woafo J. Vib. Acoust. 133 061018 (2011)

    Article  Google Scholar 

  11. T Kingni Sifeu, S Jafari, H Simo and P Woafo Eur. Phys. J. Plus. 76 129 (2014)

    Google Scholar 

  12. L Dasheng and Y Hiroshi Nonlinear Dyn. 68 95 (2012)

    Article  Google Scholar 

  13. H Wei, D Daweig, Z Yaqin and W Nian Optik 130 189 (2017)

    Article  Google Scholar 

  14. L Chunbiao and J C Sprott Nonlinear Dyn. 73 1335 (2013)

    Article  Google Scholar 

  15. M U Akmet and M O Fen Commun. Nonlinear Sci. Numer. Simul. 17 1929 (2012)

    Article  ADS  Google Scholar 

  16. T Otto, C Grebogi, and J A Yorke Phys Rev Lett. 64 1196 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  17. A L Sihem, S Bowong, F M Moukam Kakmeni, C Brahim and G Noureddine Commun. Nonlinear Sci. Numer. Simulat. 12 1504 (2007)

    Article  Google Scholar 

  18. G P Jiang, W X Zheng Chaos Solitons Fractals 21 93 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  19. R Chacon Eur. Phys. J. B 65 207 (2002)

    Article  ADS  Google Scholar 

  20. R Ferma, Chaos 12 1027 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  21. M T Yassen, Chaos Solitons Fractals 26 913 (2015)

    Article  ADS  Google Scholar 

  22. A Alasty and H Slarieh Chaos Solitons Fractals 31 292 (2001)

    Article  ADS  Google Scholar 

  23. W Ruiqi, D Jin and J Zhujun Chaos Solitons Fractals 27 249 (2006)

    Article  MathSciNet  Google Scholar 

  24. S Anjali, Vinod, Patidar, Purohit, K G Sud Commun. Nonlinear Sci. Numer. Simul. 17 2254 (2012)

  25. Z Meng, G Li, B P Wang and P Hao Comput. Struct. 146 43 (2015)

    Article  Google Scholar 

  26. Z Meng, G Li, D Yang and L Zhan Struct Multidisc. Optim. 55 12 (2017)

    Article  Google Scholar 

  27. K Ivana and J B Michael, Nonlinear Oscillators and their Behaviour (New York: Wiley) (2011)

    MATH  Google Scholar 

  28. C A Kitio kwuimy, C Nataraj and G Litak, Chaos 21 043113 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  29. L Longsuo and Y Hedan Chaos Solitons Fractals 44 498 (2011)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by CV Raman international fellowship for African Researchers. The first author gratefully acknowledges the hospitality received at the control of vibration laboratory of the Department of Mechanical Engineering of the Indian Institute of Technology Delhi.

Author information

Authors and Affiliations

  1. Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics, Faculty of Science, P. O. Box 812, Yaoundé, Cameroon

    H. Simo

  2. Department of Mechanical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India

    H. Simo & J. K. Dutt

Authors
  1. H. Simo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. K. Dutt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Simo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Simo, H., Dutt, J.K. Effects of depth potential on the dynamics of Duffing system and chaos control: numerical and electronic implementation. Indian J Phys 94, 361–370 (2020). https://doi.org/10.1007/s12648-019-01451-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01451-5

Keywords

PACS No.

Search

Navigation