Skip to main content
SpringerLink
Log in

Investigation and realization of novel chaotic system with one unstable equilibrium and symmetric coexisting attractors

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

Abstract

In this paper, a novel four-dimensional chaotic system with three quadratic nonlinearities and only one unstable equilibrium is reported. The dynamical behaviors with respect to system parameters and initial conditions are analyzed. It shows that the novel system performs periodic, quasi-periodic and chaotic motions with the variation of parameters and generates a pair of symmetric coexisting attractors for different initial conditions. Moreover the circuit implementation and impulsive synchronization control of the system are well investigated with the achievement of some theoretical and numerical 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
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability Statement

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

References

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

    Article  ADS  Google Scholar 

  2. O.E. Rössler, Phys. Lett. A 57, 397 (1976)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  4. C.P. Silva, IEEE Trans. Circ. Syst. I 40, 675 (1993)

    Article  ADS  Google Scholar 

  5. G. Li, X. Chen, Commun. Nonlinear Sci. Numer. Simul. 14, 194 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. L. Jiang, J. Sun, Chaos Solit. Fract. 32, 150 (2007)

    Article  ADS  Google Scholar 

  7. J.C. Sprott, Phys. Rev. E 50, 647 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  8. J.C. Sprott, Am. J. Phys. 65, 537 (1997)

    Article  ADS  Google Scholar 

  9. Y.X. Li, W.K.S. Wang, G. Chen, Int. J. Bifurc. Chaos 15, 3367 (2005)

    Article  Google Scholar 

  10. A. Atangana, G. Bouallegue, K. Bouallegue, Solit. Fract. Chaos. 134, 109722 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. V.T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, Eur. Phys. J. Spec. Top. 224, 1507 (2015)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  Google Scholar 

  16. N.V. Stankevich, N.V. Kuznetsov, G.A. Leonov, L.O. Chua, Int. J. Bifurc. Chaos 27, 1730038 (2017)

  17. Q. Lai, B. Norouzi, F. Liu, Solit. Fract. Chaos 114, 230 (2018)

    Article  ADS  Google Scholar 

  18. G.D. Leutcho, J. Kengne, Solit. Fract. Chaos 113, 275 (2018)

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

    Article  MathSciNet  Google Scholar 

  20. P. Prakasha, K. Rajagopalb, J.P. Singha, B.K. Roy, Int. J. Electron. Commun. 92, 111 (2018)

    Article  Google Scholar 

  21. B.A. Mezatio, M.T. Motchongom, B.R.W. Tekam, R. Kengne, R. Tchitnga, A. Fomethe, Solit. Fract. Chaos 120, 100 (2019)

    Article  ADS  Google Scholar 

  22. J.C. Sprott, X. Wang, G. Chen, Int. J. Bifurc. Chaos 23, 1350093 (2013)

    Article  Google Scholar 

  23. X. Zhong, M. Peng, C.K. Tse, S. Guo, M. Shahidehpour, Appl. Math. Comput. 268, 138 (2015)

    MathSciNet  Google Scholar 

  24. P.R. Sharma, M.D. Shrimali, A. Prasad, N.V. Kuznetsov, G.A. Leonov, Eur. Phys. J. Spec. Top. 224, 1485 (2015)

    Article  Google Scholar 

  25. O.S. Ojoniyi, A.N. Njah, Solit. Fract. Chaos 87, 172 (2016)

    Article  ADS  Google Scholar 

  26. J. Lu, G. Chen, Int. J. Bifurc. Chaos 12, 659 (2002)

    Article  Google Scholar 

  27. B. Liu, Z. Sun, Y. Luo, Y. Zhong, Phys. A 531, 121725 (2019)

    Article  MathSciNet  Google Scholar 

  28. S. Chen, Q. Yang, C. Wang, Solit. Fract. Chaos 20, 751 (2004)

    Article  ADS  Google Scholar 

  29. L. Xu, S.S. Ge, Appl. Math. Lett. 53, 52 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Jian-Jun He

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

    Bang-Cheng Lai

Authors
  1. Jian-Jun He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bang-Cheng Lai
    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

He, JJ., Lai, BC. Investigation and realization of novel chaotic system with one unstable equilibrium and symmetric coexisting attractors. Eur. Phys. J. Spec. Top. 230, 1855–1862 (2021). https://doi.org/10.1140/epjs/s11734-021-00124-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00124-x

Search

Navigation