Advertisement

Chaotic oscillator based on memcapacitor and meminductor

  • Xiaoyuan WangEmail author
  • Jun Yu
  • Chenxi Jin
  • Herbert Ho Ching Iu
  • Simin Yu
Original Paper
  • 42 Downloads

Abstract

Memcapacitor and meminductor are two new nonlinear memory circuit components defined on the basis of memristor. In the absence of physical devices of memcapacitor and meminductor, applying their equivalent circuit models into actual circuits to explore the characteristics of memcapacitor- and meminductor-based nonlinear circuits is meaningful. In this paper, a nonlinear oscillating circuit is designed based on the given nonvolatile memcapacitor and meminductor models, whose memory characteristics are analyzed using POP method in detail, and a series of dynamic characteristics of the novel chaotic circuit are analyzed, including Poincaré section, equilibrium point, system stability, bifurcation diagrams, Lyapunov exponent spectrums and dynamic map of the system. By analyzing the influence of parameters on system dynamics, the evolutionary law of the system is obtained, which helps to better use of this chaotic oscillator in possible application areas like communication encryption and synchronization approach dependent on the initial setting. In particular, coexisting attractors are found under different initial values, by drawing the attractive basin, four different types of attractors in the system are discovered, and from the attractive basin, the evolutionary process of the system under different initial values is obtained. Finally, the validity of the system is verified by DSP experiment, and the experimental results are consistent with the theoretical analysis.

Keywords

Chaos Chaotic oscillator Coexisting attractors Memcapacitor Meminductor 

Notes

Acknowledgements

This work was supported by the Natural Science Foundation of Zhejiang Province (Grant No. LY18F010012) and the National Natural Science Foundation of China (Grant Nos. 61871429, 61771176).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  2. 2.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor is found. Nature 459, 80–83 (2008)CrossRefGoogle Scholar
  3. 3.
    Chua, L.O.: The introductory talk. In: Memristor and Memristive System Symposium, pp. 361–372 (2008)Google Scholar
  4. 4.
    Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1724 (2009)CrossRefGoogle Scholar
  5. 5.
    Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurc. Chaos 20, 1567–1580 (2010)CrossRefGoogle Scholar
  7. 7.
    Zhong, G.Q.: Implementation of Chua’s circuit with a cubic nonlinearity. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 41, 934–941 (1994)CrossRefGoogle Scholar
  8. 8.
    Wang, G.Y., Zang, S.C., Wang, X.Y., Yuan, F., Iu, H.H.C.: Memcapacitor model and its application in chaotic oscillator with memristor. Chaos 27, 013110 (2017)CrossRefzbMATHGoogle Scholar
  9. 9.
    Buscarino, A., Fortuna, L., Frasca, M., Gambuzza, L.V.: A chaotic circuit based on Hewlett-Packard memristor. Chaos 22, 023136 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Muthuswamy, B.: Implementing memristor based chaotic circuits. Int. J. Bifurc. Chaos 20, 1335–1350 (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Iu, H.H.C., Yu, D.S., Fitch, A.L., Sreeram, V., Chen, H.: Controlling chaos in a memristor based circuit. IEEE Trans. Circuits Syst. I Regul. Pap. 58, 1337–1344 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Muthuswamy, B., Kokate, P.P.: Memristor-based chaotic circuits. IETE Tech. Rev. 26, 417–429 (2009)CrossRefGoogle Scholar
  13. 13.
    Fitch, A.L., Yu, D.S., Iu, H.H.C., Sreeram, V.: Hyperchaos in a memristor-based modified canonical Chua’s circuit. Int. J. Bifurc. Chaos 22, 1250133 (2012)CrossRefzbMATHGoogle Scholar
  14. 14.
    Pham, V.T., Jafari, S., Kapitaniak, T.: Constructing a chaotic system with an Infinite number of equilibrium points. Int. J. Bifurc. Chaos 26, 1650225 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wu, F.Q., Ma, J., Ren, G.D.: Synchronization stability between initial-dependent oscillators with periodical and chaotic oscillation. J. Zhejiang Univ. Sci. A (Appl. Phys. Eng.) 19, 889–903 (2018)CrossRefGoogle Scholar
  16. 16.
    Wang, C.N., Ma, J.: A review and guidance for pattern selection in spatiotemporal system. Int. J. Mod. Phys. B 32, 1830003 (2018)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Fitch, A.L., Iu, H.H.C., Yu, D.S.: Chaos in a memcapacitor based circuit. In: IEEE International Symposium on Circuits and Systems (ISCAS), pp. 482–485 (2014)Google Scholar
  18. 18.
    Yuan, F., Wang, G.Y., Jin, P.P.: Study on dynamical characteristics of a meminductor model and its meminductor-based oscillator. Acta Phys. Sin. 64, 210504 (2015)Google Scholar
  19. 19.
    Hu, Z.H, Li, Y.X, Jia, L., Yu, J.B.: Chaos in a charge-controlled memcapacitor circuit. In: International Conference on Communications, Circuits and Systems, pp. 828–831 (2010)Google Scholar
  20. 20.
    Wang, G.Y., Jin, P.P., Wang, X.W., Shen, Y.R., Yuan, F., Wang, X.Y.: A flux-controlled model of meminductor and its application in chaotic oscillator. Chin. Phys. B 25, 090502 (2016)CrossRefGoogle Scholar
  21. 21.
    Zhu, H.T., Duan, S.K., Wang, L.D., Yang, T., Tan, J.P.: The nonlinear meminductor models with its study on the device parameters variation. In: Seventh International Conference on Information Science and Technology, pp. 497–503. IEEE (2017)Google Scholar
  22. 22.
    Riaza, R.: First order mem-circuits: modeling, nonlinear oscillations and bifurcations. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 1570–1583 (2013)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wang, X.Y., Fitch, A.L., Iu, H.H.C., Qi, W.G.: Design of a memcapacitor emulator based on a memristor. Phys. Lett. A 376, 394–399 (2012)CrossRefzbMATHGoogle Scholar
  24. 24.
    Liang, Y., Yu, D.S., Chen, H.: A novel meminductor emulator based on analog circuits. Acta Phys. Sin. 62, 158501 (2013)Google Scholar
  25. 25.
    Mou, J., Sun, K.H., Ruan, J.Y., He, S.B.: A nonlinear circuit with two memcapacitors. Nonlinear Dyn. 86, 1735–1744 (2016)CrossRefGoogle Scholar
  26. 26.
    Karthikeyn, R., Sajad, J., Ashokkumar, A.K., Biniyam, A.: Hyperchaotic memcapacitor oscillator with infinite equilibria and coexisting attractors. Circuits Syst. Signal Process. 7, 824–827 (2018)MathSciNetGoogle Scholar
  27. 27.
    Rajagopal, K., Karthikeyan, A., Srinivasan, A.: Bifurcation and chaos in time delayed fractional order chaotic memfractor oscillator and its sliding mode synchronization with uncertainties. Chaos Solitons Fractals 103, 347–356 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Rajagopal, K., Akgul, A., Jafari, S., Aricioglu, B.: A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications. Nonlinear Dyn. 91, 957–974 (2018)CrossRefGoogle Scholar
  29. 29.
    Yuan, F., Wang, G.Y., Wang, X.W.: Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis. Chaos 27, 033103 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Chua, L.O.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24, 319–368 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Electronics and InformationHangzhou Dianzi UniversityHangzhouPeople’s Republic of China
  2. 2.School of Electrical, Electronic and Computer EngineeringThe University of Western AustraliaPerthAustralia

Personalised recommendations