Skip to main content
SpringerLink
Log in

Dynamic analysis, circuit implementation and passive control of a novel four-dimensional chaotic system with multiscroll attractor and multiple coexisting attractors

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, we construct a novel 4D autonomous chaotic system with four cross-product nonlinear terms and five equilibria. The multiple coexisting attractors and the multiscroll attractor of the system are numerically investigated. Research results show that the system has various types of multiple attractors, including three strange attractors with a limit cycle, three limit cycles, two strange attractors with a pair of limit cycles, two coexisting strange attractors. By using the passive control theory, a controller is designed for controlling the chaos of the system. Both analytical and numerical studies verify that the designed controller can suppress chaotic motion and stabilise the system at the origin. Moreover, an electronic circuit is presented for implementing the chaotic 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. S Rinaldi, S Muratori and Y Kuznetsov, Bull. Math. Biol. 55, 15 (1993)

    Article  Google Scholar 

  2. S M Henson, Phys. D 140, 33 (2000)

    Article  MathSciNet  Google Scholar 

  3. T Onozaki, G Sieg and M Yokoo, J. Econ. Dyn. Control 27, 1917 (2003)

    Article  Google Scholar 

  4. S Tang, Y Xiao and R A Cheke, Theor. Popul. Biol. 73, 181 (2008)

    Article  Google Scholar 

  5. J L Schwartz, N Grimault, J M Hupe, B C Moore and D Pressnitzer, Phil. Trans. R. Soc. B 367, 896 (2012)

    Article  Google Scholar 

  6. C B Li and J C Sprott, Int. J. Bifurc. Chaos 24, 1450131 (2014)

    Article  Google Scholar 

  7. Q Lai and S Chen, Int. J. Syst. Control Autom. Syst. 14, 1124 (2016)

    Article  Google Scholar 

  8. Q Lai and S Chen, Int. J. Bifurc. Chaos 26, 1650177 (2016)

    Article  Google Scholar 

  9. D C Braga and L F Mello, Int. J. Bifurc. Chaos 23, 1350203 (2013)

    Article  Google Scholar 

  10. V K Tamba, H B Fotsin, J Kengne, E B Ngouonkadi and P K Talla, Int. J. Dyn. Control 10, 1 (2016)

    Google Scholar 

  11. V T Pham, C Volos, S Jafari and T Kapitaniak, Nonlinear Dyn. 87, 2001 (2017)

    Article  Google Scholar 

  12. J C Sprott, S Jafari, A J M Khalaf and T Kapitaniak, Eur. Phys. J. Spec. Top.  226, 1979 (2017)

    Article  Google Scholar 

  13. C B Li and J C Sprott, Optik 127, 10389 (2016)

    Article  ADS  Google Scholar 

  14. C B Li, J C Sprott, A Akgul, H H C Iu and Y Zhao, Chaos 27, 083101 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  15. C B Li, X Wang and G Chen, Nonlinear Dyn, https://doi.org/10.1007/s11071-017-3729-1 (2017)

  16. Q Lai and S Chen, Optik 127, 3000 (2016)

    Article  ADS  Google Scholar 

  17. S T Kingnia, S Jafari, V T Pham and P Woafo, Math. Comput. Simul. 132, 172 (2017)

    Article  Google Scholar 

  18. M Shahzad, V T Pham, M A Ahmad, S Jafari and F Hadaeghi, Eur. Phys. J. Spec. Top. 224, 1637 (2015)

    Article  Google Scholar 

  19. B C Bao, Q D Li, N Wang and Q Xu, Chaos 26, 043111 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. Y Lin, C Wang, H He and L L Zhou, Pramana – J. Phys. 86, 801 (2016)

    Article  ADS  Google Scholar 

  21. M F Danca, M I Feckan, N Kuznetsov and G Chen, Int. J. Bifurc. Chaos 26, 1650038 (2016)

    Article  Google Scholar 

  22. Q Lai, A Akgul, X W Zhao and H Pei, Int. J. Bifurc. Chaos 27, 1750142 (2017)

    Article  Google Scholar 

  23. S Jafari, V T Pham and T Kapitaniak, Int. J. Bifurc. Chaos 26, 1650031 (2016)

    Article  Google Scholar 

  24. F R Tahir, S Jafari, V T Pham, C Volos and X Wang, Int. J. Bifurc. Chaos 25, 1550056 (2016)

    Article  Google Scholar 

  25. C L Li, S M Yu and X S Luo, Int. J. Bifurc. Chaos 23, 1350170 (2013)

    Article  Google Scholar 

  26. G L Li and X Y Chen, Commun. Nonlinear Sci. Numer. Simul. 14, 194 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  27. C X Zhang, S M Yu and Y Zhang, Int. J. Mod. Phys. B 25, 2183 (2011)

    Article  ADS  Google Scholar 

  28. E Ott, C Grebogi and J A Yorke, Phys. Rev. Lett. 64, 1196 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  29. C Li and Y Tong, Pramana – J. Phys. 80, 583 (2013)

    Article  ADS  Google Scholar 

  30. A Nourian and S Balochian, Pramana – J. Phys. 86, 1401 (2016)

    Article  ADS  Google Scholar 

  31. M Feki, Chaos Solitons Fractals 15, 883 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  32. M Rafikov and J M Balthazar, Commun. Nonlinear Sci. Numer. Simul. 13, 1246 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  33. S Chen, Q Yang and C Wang, Chaos Solitons Fractals 20, 751 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  34. D R Zhu, C X Liu and B N Yan, Chin. Phys. B 21, 090509 (2012)

    Article  ADS  Google Scholar 

  35. X Chen and C X Liu, Nonlinear Anal. Real World Appl. 11, 683 (2010)

    Article  MathSciNet  Google Scholar 

  36. G M Mahmoud, E E Mahmoud and A A Arafa, J. Vib. Control 19, 1061 (2012)

    Article  Google Scholar 

  37. Q J Zhang and J A Lu, Chin. Phys. B 17, 1674 (2008)

    Google Scholar 

  38. X J Wu, J S Liu and G Chen, Nonlinear Dyn. 53, 45 (2008)

    Article  Google Scholar 

  39. W B Liu and G Chen, Int. J. Bifurc. Chaos 13, 261 (2003)

    Article  Google Scholar 

  40. A Wolf, J B Swift, H L Swinney and J A Vastano, Physica D 16, 285 (1985)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Technology, East China Jiaotong University, Nanchang, 330100, China

    Bang-Cheng Lai

  2. College of Applied Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China

    Jian-Jun He

Authors
  1. Bang-Cheng Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-Jun He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bang-Cheng Lai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lai, BC., He, JJ. Dynamic analysis, circuit implementation and passive control of a novel four-dimensional chaotic system with multiscroll attractor and multiple coexisting attractors. Pramana - J Phys 90, 33 (2018). https://doi.org/10.1007/s12043-018-1525-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1525-1

Keywords

PACS No

Search

Navigation