Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 893–903 | Cite as

Chaotic and periodic bursting phenomena in a memristive Wien-bridge oscillator

  • Huagan Wu
  • Bocheng BaoEmail author
  • Zhong Liu
  • Quan Xu
  • Pan Jiang
Original Paper


Bursting, an important communication activity in biological neurons and endocrine cells, has been widely found in fast-slow dynamical systems. In this paper, a modified second-order generalized memristor, memristive diode bridge cascaded with LC network, is presented and its fingerprints of the pinched hysteresis loops are analyzed. By replacing the parallel resistor with the modified generalized memristor, a novel memristive Wien-bridge oscillator is constructed and its mathematical model is established, from which the dynamical behaviors of symmetric chaotic and periodic bursting oscillations are observed and the corresponding bifurcation mechanisms are explained. Based on a hardware realization circuit, experimental observations are performed, which verify the numerical simulations.


Bursting Wien-bridge oscillator Memristive diode bridge Bifurcation 



This work was supported by the grants from the National Natural Science Foundations of China (Grant No. 51277017) and the Natural Science Foundations of Jiangsu Province (Grant No. BK2012583).


  1. 1.
    Williams, R.S.: How we found the missing memristor. IEEE Spectr. 45, 28–35 (2008)CrossRefGoogle Scholar
  2. 2.
    Duan, S.K., Hu, X.F., Wang, L.D., Li, C.D.: Analog memristive memory with applications in audio signal processing. Sci. China Info. Sci. 57, 1–15 (2014)CrossRefGoogle Scholar
  3. 3.
    Vaynshteyn, M., Lanis, A.: Applications of electrochemical elements in systems of artificial intelligence. Nat. Sci. 11, 45–51 (2013)Google Scholar
  4. 4.
    Ebong, I.E., Mazumder, P.: CMOS and memristor-based neural network design for position detection. Proc. IEEE 100, 2050–2060 (2012)CrossRefGoogle Scholar
  5. 5.
    Li, Q.D., Hu, S.Y., Tang, S., Zeng, G.: Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation. Int. J. Circ. Theor. Appl. 42, 1172–1188 (2014)CrossRefGoogle Scholar
  6. 6.
    Iu, H.H.C., Yu, D.S., Fitch, A.L., Sreeram, V., Chen, H.: Controlling chaos in a memristor based circuit using a twin-T notch filter. IEEE Trans. Circuits Syst. I Regul. Pap. 58, 1337–1344 (2011)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Bao, B.C., Ma, Z.H., Xu, J.P., Liu, Z., Xu, Q.: A simple memristor chaotic circuit with complex dynamics. Int. J. Bifurc. Chaos 21, 2629–2645 (2011)CrossRefzbMATHGoogle Scholar
  8. 8.
    Chen, M., Yu, J.J., Yu, Q., Li, C.D., Bao, B.C.: A memristive diode bridge-based canonical Chua’s circuit. Entropy 16, 6464–6476 (2014)CrossRefGoogle Scholar
  9. 9.
    Bao, B.C., Jiang, P., Wu, H.G., Hu, F.W.: Complex transient dynamics in periodically forced memristive Chua’s circuit. Nonlinear Dyn. 79, 2333–2343 (2015)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Yu, Q., Bao, B.C., Hu, F.W., Xu, Q., Chen, M., Wang, J.: Wien-bridge chaotic oscillator based on first-order generalized memristor. Acta Phys. Sin. 24, 240504 (2014). (in Chinese)Google Scholar
  11. 11.
    Buscarino, A., Fortuna, L., Frasca, M., Gambuzza, L.V.: A chaotic circuit based on Hewlett-Packard memristor. Chaos 22, 023136 (2012)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  13. 13.
    Kim, H., Sah, M.P., Yang, C.J., Cho, S., Chua, L.O.: Memristor emulator for memristor circuit applications. IEEE Trans. Circuits Syst. I Regul. Pap. 59, 2422–2431 (2012)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Yu, D.S., Liang, Y., Chen, H., Iu, H.H.C.: Design of a practical memcapacitor emulator without grounded restriction. IEEE Trans. Circuits Syst. II Express Briefs 60, 207–211 (2013)CrossRefGoogle Scholar
  15. 15.
    Sanchez-Lopez, C., Mendoza-Lopez, J.: A floating analog memristor emulator circuit. IEEE Trans. Circuits Syst. II Express Briefs 61, 309–313 (2014)CrossRefGoogle Scholar
  16. 16.
    Wang, X.Y., Fitch, A.L., Iu, H.H.C., Sreeram, V., Qin, W.G.: Implementation of an analogue model of a memristor based on a light-dependent resistor. Chin. Phys. B 21, 108501 (2012)CrossRefGoogle Scholar
  17. 17.
    Corinto, F., Ascoli, A.: Memristive diode bridge with LCR filter. Electron. Lett. 48, 824–825 (2012)CrossRefGoogle Scholar
  18. 18.
    Bao, B.C., Yu, J.J., Hu, F.W., Liu, Z.: Generalized memristor consisting of diode bridge with first order parallel RC filter. Int. J. Bifurc. Chaos 24, 1450143 (2014)CrossRefzbMATHGoogle Scholar
  19. 19.
    Izhikevich, E.M.: Neural excitability, spiking and bursting. Int. J. Bifurc. Chaos 10, 1171–1266 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Vries, G.: Bursting as an emergent phenomenon in coupled chaotic maps. Phys. Rev. E 64, 051914 (2001)CrossRefGoogle Scholar
  21. 21.
    Dana, S.K., Sethia, G.C., Sen, A.: Bursting near homoclinic bifurcation in two coupled Chua oscillators. Int. J. Bifurc. Chaos 17, 3437–3442 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Wang, Z.L., Shi, X.R.: Chaotic bursting lag synchronization of Hindmarsh-Rose system via a single controller. Appl. Math. Comput. 215, 1091–1097 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    Ji, Y., Bi, Q.S.: Symmetric bursting behaviour in non-smooth Chua’s circuit. Chin. Phys. B 19, 080510 (2010)CrossRefGoogle Scholar
  24. 24.
    Zhang, Z.D., Liu, B.B., Bi, Q.S.: Non-smooth bifurcations on the bursting oscillations in a dynamic system with two timescales. Nonlinear Dyn. 79, 195–203 (2015)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Bi, Q.S., Ma, R., Zhang, Z.D.: Bifurcation mechanism of the bursting oscillations in periodically excited dynamical system with two time scales. Nonlinear Dyn. 79, 101–110 (2015)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Zhou, G.H., Bao, B.C., Xu, J.P.: Complex dynamics and fast-slow scale instability in current-mode controlled buck converter with constant current load. Int. J. Bifurc. Chaos 23, 1350062 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  27. 27.
    Chua, L.O.: The fourth element. Proc. IEEE 100, 1920–1927 (2012)CrossRefGoogle Scholar
  28. 28.
    Adhikari, S.P., Sah, M.P., Kim, H., Chua, L.O.: Three fingerprints of memristor. IEEE Trans. Circuits Syst. I Regul. Pap 60, 3008–3021 (2013)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Talukdar, A., Radwan, A.G., Salama, K.N.: Generalized model for memristor-based Wien family oscillators. Microelectron. J. 42, 1032–1038 (2011)CrossRefGoogle Scholar
  30. 30.
    Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Phys. D 16, 285–317 (1985)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Huagan Wu
    • 1
  • Bocheng Bao
    • 2
    Email author
  • Zhong Liu
    • 1
  • Quan Xu
    • 2
  • Pan Jiang
    • 2
  1. 1.School of Electronic and Optical EngineeringNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Information Science and EngineeringChangzhou UniversityChangzhouChina

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