Skip to main content
SpringerLink
Log in

A new chaotic system with different equilibria and attractors

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

This paper presents an interesting four-dimensional chaotic system with different equilibria and attractors. The proposed system has three quadratic nonlinearities and has no equilibrium, three equilibria and infinite equilibria for different regions of system parameters. As the values of parameters change, the system performs stable, periodic and chaotic states. Also it has period-doubling bifurcation which leads to chaos and has Hopf bifurcation which makes the system loses stability. Moreover, the system generates hidden chaotic attractor when it has no equilibria and generates coexisting chaotic attractors for different initial values. The electronic circuit implementation of the system is given to illustrate the corresponding dynamical properties of the 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

Similar content being viewed by others

Data Availability Statement

My manuscript has no associated data or the data will not be deposited.

References

  1. M.F. Hassan, M. Hammuda, J. Frank. Inst. 356, 6697 (2019)

    Article  Google Scholar 

  2. S. Nasr, H. Mekki, K. Bouallegue, Chaos Soliton Fractal 118, 366 (2019)

    Article  ADS  Google Scholar 

  3. C. Li, G. Luo, K. Qin, C. Li, Nonlinear Dyn. 87, 127 (2017)

    Article  Google Scholar 

  4. A. Adewumi, J. Kagamba, A. Alochukwu, Math. Probl. Eng. 2016, 5656734 (2016)

  5. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  7. G. Chen, D. Lai, IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 44, 250 (1997)

    Article  Google Scholar 

  8. M.S. Anwar, G.K. Sar, A. Ray, D. Ghosh, Eur. Phys. J. Spec. Top. 229, 1343 (2020)

    Article  Google Scholar 

  9. Q. Lai, B. Norouzi, F. Liu, Chaos Solitons Fractals 114, 230 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  10. Q. Lai, Z. Wan, P.D. Kamdem Kuate, H. Fotsin, Commun. Nonlinear Sci. Numer. Simul. 89, 105341 (2020)

    Article  MathSciNet  Google Scholar 

  11. A.N. Negoua, J. Kengne, Int. J. Electron. Commun. 90, 1 (2018)

    Article  Google Scholar 

  12. A. Algaba, M. Merino, B.W. Qin, A.J. Rodriguez-Luis, Phys. Lett. A 383, 1441 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  13. J.C. Sprott, S. Jafari, V.T. Pham, Z.S. Hosseini, Phys. Lett. A 379, 2030 (2015)

    Article  MathSciNet  ADS  Google Scholar 

  14. S. Jafari, J.C. Sprott, S.M. Reza Hashemi Golpayegani, Phys. Lett. A 377, 699 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  15. S. Yu, W.K.S. Tang, J. Lu, G. Chen, Int. J. Bifurc. Chaos 20, 29 (2010)

    Article  ADS  Google Scholar 

  16. Q. Lai, P.D. Kamdem Kuate, F. Liu, H.H.C. Iu, IEEE Trans. Circ. Syst. II 67, 129 (2020)

    Google Scholar 

  17. X. Wang, G. Chen, Nonlinear Dyn. 71, 429 (2013)

    Article  Google Scholar 

  18. M. Molaie, S. Jafari, Int. J. Bifurc. Chaos 23, 1350188 (2013)

    Article  Google Scholar 

  19. B.A. Mezatio, M.T. Motchongom, B.R.W. Tekam, R. Kengne, R. Tchitnga, A. Fomethe, Chaos Solitons Fractals. 120, 110 (2019)

    Article  ADS  Google Scholar 

  20. V.T. Pham, A. Akgul, C. Volos, S. Jafari, T. Kapitaniak, AEU-Int. J. Electr. Commun. 78, 134 (2017)

    Article  Google Scholar 

  21. F. Nazarimehr, K. Rajagopal, A.J.M. Khalaf, A. Alsaedi, V.T. Pham, T. Hayat, Chaos Solitons Fractals. 115, 7 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  22. M. Tuna, A. Karthikeyan, K. Rajagopal, M. Alcin, I. Koyuncu, AEU-Int. J. Electr. Commun. 112 (2019)

  23. J.P. Singh, B.K. Roy, S. Jafari, Chaos Solitons Fractals 106, 243 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  24. V.T. Pham, C. Volos, S. Jafari, Z. Wei, X. Wang, Int. J. Bifurc. Chaos 24, 1450073 (2014)

    Article  Google Scholar 

  25. Q. Lai, S. Chen, Int. J. Bifur. Chaos 26 (2016)

  26. J. Kengne, Z.T. Njitacke, H.B. Fotsin, Nonlinear Dyn. 83, 751 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Public Teaching, Nanchang Institute of Technology, Nanchang, 330044, China

    Hai-Yong Cao

  2. Department of Basic Sciences, Nanchang Jiaotong Institute, Nanchang, 330100, China

    Lan Zhao

Authors
  1. Hai-Yong Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lan Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, HY., Zhao, L. A new chaotic system with different equilibria and attractors. Eur. Phys. J. Spec. Top. 230, 1905–1914 (2021). https://doi.org/10.1140/epjs/s11734-021-00123-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00123-y

Search

Navigation