Skip to main content
SpringerLink
Log in

Complicated dynamics in a memristor-based RLC circuit

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

Abstract

As the fourth basic circuit element, the memristor is usually employed to design chaotic circuit for the special electrical properties. This paper introduces a memristor-based RLC oscillation circuit with fourth-order differential equation. Basic dynamical properties of the system are revealed by analyzing phase portrait, time-domain waveform, Poincaré map, equilibrium point, bifurcation diagram and Lyapunov exponent. Specially, coexisting attractor with the variation of initial value is explored in this system, which means the multi-stability arises. And it is also found that there exists complicated transient dynamical behavior for some initial conditions and parameters, which completely differs from the existed modes of transient chaos and transient period.

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

Similar content being viewed by others

References

  1. L.O. Chua, IEEE Trans. Circuits Theory 18, 507 (1971)

    Article  Google Scholar 

  2. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)

    Article  ADS  Google Scholar 

  3. T.F. Fonzin, K. Srinivasan, J. Kengne, F.B. Pelap, A.E.U. Int, J. Electron. C 90, 110 (2018)

    Google Scholar 

  4. W. Feng, Y.G. He, C.L. Li, X.M. Su, X.Q. Chen, Complexity 2018, 1 (2018)

    Google Scholar 

  5. V.T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov, T.M. Hoang, Eur. Phys. J. Special Topics 225, 127 (2016)

    Article  ADS  Google Scholar 

  6. M. Lv, C.N. Wang, G.D. Ren, J. Ma, X.L. Song, Nonlinear Dyn. 85, 1479 (2016)

    Article  Google Scholar 

  7. Y. Xu, Y. Jia, J.B. Kirunda, Complexity 2018, 1 (2018)

    Google Scholar 

  8. S. Zhu, L. Wang, S. Duan, Neurocomputing 227, 149 (2017)

    Article  Google Scholar 

  9. G. Peng, F. Min, Nonlinear Dyn. 90, 1607 (2017)

    Article  Google Scholar 

  10. B. Bao, N. Wang, Q. Xu, H. Wu, Y. Hu, I.E.E.E. Trans, Circ. Syst. II 64, 977 (2017)

    Google Scholar 

  11. B. Muthuswamy, L.O. Chua, Int. J. Bifurc. Chaos 20, 1567 (2010)

    Article  Google Scholar 

  12. L. Teng, H.H.C. Iu, X.Y. Wang, X.K. Wang, Nonlinear Dyn. 77, 231 (2014)

    Article  Google Scholar 

  13. B. Bao, Z. Ma, J. Xu, Z. Liu, Q. Xu, Int. J. Bifurc. Chaos 21, 2629 (2011)

    Article  Google Scholar 

  14. B. Bao, Q. Xu, H. Bao, M. Chen, Electron. Lett. 52, 1008 (2016)

    Article  Google Scholar 

  15. F. Yuan, G. Wang, X. Wang, Chaos 26, 507 (2016)

    Google Scholar 

  16. X. Wang, S. Vaidyanathan, C. Volos, V.T. Pham, T. Kapitaniak, Nonlinear Dyn. 1, 1 (2012)

    Google Scholar 

  17. J. Kengne, Int. J. Bifurc. Chaos 25, 4285 (2015)

    Article  MathSciNet  Google Scholar 

  18. N.H. Alombah, H. Fotsin, K. Romanic, Int. J. Bifurc. Chaos 27, 1750067 (2017)

    Article  Google Scholar 

  19. X. Zhong, M. Peng, M. Shahidehpour, S. Guo, IEEE Access 99, 1 (2018)

    Google Scholar 

  20. L. Zhou, C.H. Wang, X. Zhang, W. Yao, Int. J. Bifurc. Chaos 28, 1850050 (2018)

    Article  Google Scholar 

  21. J. Ruan, K. Sun, J. Mou, S. He, L. Zhang, Eur. Phys. J. Plus 133, 3 (2018)

    Article  Google Scholar 

  22. J. Kengne, A.N. Negou, Z.T. Njitacke, Nonlinear Dyn. 27, 1008 (2017)

    Google Scholar 

  23. Z. Wang, W. Sun, Z. Wei, S. Zhang, Nonlinear Dyn. 82, 577 (2015)

    Article  Google Scholar 

  24. H. Bao, N. Wang, B. Bao, M. Chen, P. Jin, G. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  25. N.H. Alombah, H. Fotsin, K. Romanic, E.M. Ngouonkadi, T. Nguazon, Int. J. Bifurc. Chaos 26, 1650128 (2016)

    Article  Google Scholar 

  26. G.Y. Wang, J.L. He, F. Yuan, C.J. Peng, Chin. Phys. Lett. 30, 110506 (2013)

    Article  ADS  Google Scholar 

  27. M. Itoh, L.O. Chua, Int. J. Bifurc. Chaos 18, 3183 (2008)

    Article  Google Scholar 

  28. B.C. Bao, P.Y. Wu, H. Bao, Q. Xu, M. Chen, Chaos Soliton Fractals 106, 161 (2018)

    Article  ADS  Google Scholar 

  29. Z. Galias, Int. J. Bifurc. Chaos 24, 173 (2014)

    Article  MathSciNet  Google Scholar 

  30. Z. Aram, S. Jafari, J. Ma, J.C. Sprott, S. Zendehrouh, V.T. Pham, Commun. Nonlinear Sci. Numer. Simul. 44, 449 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  31. Y.B. Zhao, C.K. Tse, J.C. Feng, Y.C. Guo, Circ. Syst. Signal Process. 32, 1013 (2013)

    Article  Google Scholar 

  32. S. Dadras, H.R. Momeni, G. Qi, Nonlinear Dyn. 62, 391 (2010)

    Article  Google Scholar 

  33. S. Sabarathinam, C.K. Volos, K. Thamilmaran, Nonlinear Dyn. 87, 37 (2017)

    Article  Google Scholar 

  34. M.F. Danca, Nonlinear Dyn. 86, 1263 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang, 414006, P.R. China

    Chunlai Li, Yang Zhou, Yanfeng Yang, Hongmin Li, Wei Feng, Zhaoyu Li & Youli Lu

  2. School of Information and Communication Engineering, Hunan Institute of Science and Technology, Yueyang, 414006, P.R. China

    Yang Zhou, Yanfeng Yang & Youli Lu

Authors
  1. Chunlai Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yanfeng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hongmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wei Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhaoyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Youli Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunlai Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Zhou, Y., Yang, Y. et al. Complicated dynamics in a memristor-based RLC circuit. Eur. Phys. J. Spec. Top. 228, 1925–1941 (2019). https://doi.org/10.1140/epjst/e2019-800195-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2019-800195-8

Search

Navigation