The European Physical Journal Special Topics

, Volume 228, Issue 10, pp 2011–2021 | Cite as

Coexistence of periodic and strange attractor in a memristive band pass filter circuit with amplitude control

  • Yan YangEmail author
  • Kangcheng Ren
  • Hui Qian
  • Xiaoyong Yao
Regular Article
Part of the following topical collections:
  1. Memristor-based Systems: Nonlinearity, Dynamics and Applications


By replacing the cubic voltage-controlled memristor emulator with the quadratic one in an existing memristive band pass filter (BPF) chaotic circuit, a modified memristive BPF circuit with two asymmetric equilibria is proposed. A dimensionless model is used to analyse the fundamental properties. The nonlinear techniques including phase portraits, bifurcation diagrams, Lyapunov exponents, Poincaré sections, and attraction basins are used to analyse the complex dynamics. The striking feature is that this system exhibits the bi-stability phenomenon of coexisting periodic and strange attractors with adjustable amplitudes. The results of theoretical analysis are effectively verified by numerical simulations and hardware experiments.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C.B. Li, J.C. Sprott, Nonlinear Dyn. 73, 1335 (2013)CrossRefGoogle Scholar
  2. 2.
    C.B. Li, J.C. Sprott, Z.S. Yuan, H.T. Li, Int. J. Bifurc. Chaos 25, 1530025 (2015)CrossRefGoogle Scholar
  3. 3.
    C.B. Li, J.C. Sprott, H.Y. Xing, Int. J. Bifurc. Chaos 26, 1650233 (2016)CrossRefGoogle Scholar
  4. 4.
    H. Chen, A. Bayani, A. Akgul, M. Jafari, V.T. Pham, X. Wang, S. Jafari, Nonlinear Dyn. 92, 1791 (2018)CrossRefGoogle Scholar
  5. 5.
    Z.C. Wei, V.T. Pham, A.J.M. Khalaf, J. Kengne, S. Jafari, Int. J. Bifurc. Chaos 28, 1850085 (2018)CrossRefGoogle Scholar
  6. 6.
    H. Bao, T. Jiang, K.B. Chu, M. Chen, Q. Xu, B.C. Bao, Complexity 2018, 5935637 (2018)Google Scholar
  7. 7.
    M. Chen, M.X. Sun, B.C. Bao, H.G. Wu, Q. Xu, J. Wang, Nonlinear Dyn. 91, 1395 (2018)CrossRefGoogle Scholar
  8. 8.
    M. Chen, M.X. Sun, H. Bao, Y.H. Hu, B.C. Bao, IEEE Trans. Ind. Electron. (2019), DOI:
  9. 9.
    V.T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, Eur. Phys. J. Special Topics 224, 1507 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    V.T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, N. Kuznetsov, T. Hoang, Eur. Phys. J. Special Topics 225, 127 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    X. Wang, G.R. Chen, Commun. Nonlinear Sci. Numer. Simul. 17, 1264 (2012)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Z.C. Wei, P. Yu, W. Zhang, M.H. Yao, Nonlinear Dyn. 82, 131 (2015)CrossRefGoogle Scholar
  13. 13.
    Z.C. Wei, V.T. Pham, T. Kapitaniak, Z. Wang, Nonlinear Dyn. 85, 1635 (2016)CrossRefGoogle Scholar
  14. 14.
    Z.C. Wei, I. Moroz, Z. Wang, W. Zhang, Int. J. Bifurc. Chaos 27, 1730008 (2017)CrossRefGoogle Scholar
  15. 15.
    Z.C. Wei, I. Moroz, J.C. Sprott, A. Akgul, W. Zhang, Chaos 27, 033101 (2017)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    K. Barati, S. Jafari, J.C. Sprott, V.T. Pham, Int. J. Bifurc. Chaos 26, 1630034 (2016)CrossRefGoogle Scholar
  17. 17.
    S. Jafari, J.C. Sprott, M. Molaie, Int. J. Bifurc. Chaos 26, 1650098 (2016)CrossRefGoogle Scholar
  18. 18.
    B.C. Bao, T. Jiang, G.Y. Wang, P.P. Jin, H. Bao, M. Chen, Nonlinear Dyn. 89, 1157 (2017)CrossRefGoogle Scholar
  19. 19.
    K. Rajagopal, A. Karthikeyan, A. Srinivasan, Chaos Soliton Fractals 103, 347 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    K. Rajagopal, A. Akgul, S. Jafari, B. Aricioglu, Nonlinear Dyn. 91, 957 (2018)CrossRefGoogle Scholar
  21. 21.
    A. Karthikeyan, K. Rajagopal, Pramana 90, 14 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    L.O. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)CrossRefGoogle Scholar
  23. 23.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    B.C. Bao, P. Jiang, H.G. Wu, F.W. Hu, Nonlinear Dyn. 79, 2333 (2015)CrossRefGoogle Scholar
  25. 25.
    H. Bao, N. Wang, B.C. Bao, M. Chen, P.P. Jin, G.Y. Wang, Commun. Nonlinear Sci. Numer. Simul. 57, 264 (2018)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Q. Xu, Y. Lin, B.C. Bao, M. Chen, Chaos Soliton Fractals 83, 186 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    Z.T. Njitacke, J. Kengne, H.B. Fotsin, A. Nguomkam Negou, D. Tchiotsop, Chaos Soliton, Fractals 91, 180 (2016)CrossRefGoogle Scholar
  28. 28.
    T.F. Fonzin, K. Srinivasan, J. Kengne, F.B. Pelap, Int. J. Electron. Commun. (AEÜ) 90, 110 (2018)CrossRefGoogle Scholar
  29. 29.
    K. Rajagopal, H. Jahanshahi, M. Varan, I. Bayr, V.T. Pham, S. Jafari, A. Karthikeyan, Int. J. Electron. Commun. (AEÜ) 94, 55 (2018)CrossRefGoogle Scholar
  30. 30.
    K. Rajagopal, S. Arun, A. Karthikeyan, P. Duraisamy, A. Srinivasan, Int. J. Electron. Commun. (AEÜ) 95, 249 (2018)CrossRefGoogle Scholar
  31. 31.
    B.C. Bao, Q. Xu, H. Bao, M. Chen, Electron. Lett. 52, 1008 (2016)CrossRefGoogle Scholar
  32. 32.
    B.C. Bao, H. Bao, N. Wang, M. Chen, Q. Xu, Chaos Soliton Fractals 94, 102 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    N. Wang, B.C. Bao, T. Jiang, M. Chen, Q. Xu, Math. Probl. Eng. 2017, 5897286 (2017)Google Scholar
  34. 34.
    Q.D. Li, S. Tang, H.Z. Zeng, T.T. Zhou, Nonlinear Dyn. 78, 1087 (2014)CrossRefGoogle Scholar
  35. 35.
    V.T. Pham, S. Jafari, S. Vaidyanathan, C.K. Volos, X. Wang, Sci. China Tech. Sci. 59, 358 (2016)CrossRefGoogle Scholar
  36. 36.
    J. Ma, J. Tang, Nonlinear Dyn. 89, 1569 (2017)CrossRefGoogle Scholar
  37. 37.
    B.C. Bao, H. Qian, Q. Xu, M. Chen, J. Wang, Y.J. Yu, Front. Comput. Neurosci. 11, 81 (2017)CrossRefGoogle Scholar
  38. 38.
    H. Bao, A.H. Hu, W.B. Liu, B.C. Bao, IEEE Trans. Neural Netw. Learn. Syst. (2019), DOI:
  39. 39.
    B.C. Bao, N. Wang, Q. Xu, H.G. Wu, Y.H. Hu, IEEE Trans. Circuit Syst. II: Exp. Briefs 64, 977 (2017)CrossRefGoogle Scholar
  40. 40.
    X. Zhang, B.C. Bao, H. Bao, Z.M. Wu, Y.H. Hu, IEEE Access 6, 46227 (2017)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronics TechnicalChangzhou Xingyu Automotive Lighting System Co, Ltd.ChangzhouP.R. China

Personalised recommendations