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Memristor Cellular Neural Networks Computing in the Flux-charge Domain

  • Fernando Corinto
  • Mauro Forti
  • Leon O. Chua
Chapter
  • 103 Downloads

Abstract

A memristor is a nonlinear device obeying Ohm’s law but, unlike a resistor, the memristor resistance, also called memristance, depends upon the history of the voltage applied or the current flowing through it. A memristor is then both a nonlinear and a memory element in the (v, i)-domain. Another unique property is nonvolatility, namely, when current (or voltage) is turned off, the memristor can keep in memory the final value of charge, flux, or memristance, thereafter (see Chap.  2).

References

  1. 1.
    L. Chua, G. Sirakoulis, A. Adamatzky (eds.), Handbook of Memristor Networks, vol. 1 and 2 (Springer, New York, 2019)Google Scholar
  2. 2.
    H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Memristor bridge synapses. Proc. IEEE 100(6), 2061–2070 (2012)CrossRefGoogle Scholar
  3. 3.
    H. Kim, M. Sah, C. Yang, T. Roska, L.O. Chua, Neural synaptic weighting with a pulse-based memristor circuit. IEEE Trans. Circuits Syst. I. Regul. Pap. 59(1), 148–158 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Sah, H. Kim, L.O. Chua, Brains are made of memristors. IEEE Circuits Syst. Mag. 14(1), 12–36 (2014)CrossRefGoogle Scholar
  5. 5.
    R. Stanley Williams, What’s next? [The end of Moore’s law]. Comput. Sci. Eng. 19(2), 7–13 (2017)CrossRefGoogle Scholar
  6. 6.
    M.A. Zidan, J.P. Strachan, W.D. Lu, The future of electronics based on memristive systems. Nat. Electron. 1(1), 22 (2018)Google Scholar
  7. 7.
    O. Krestinskaya, A.P. James, L.O. Chua, Neuromemristive circuits for edge computing: a review. IEEE Trans. Neural Netw. Learn. Syst. 31(1), 4–23 (2020).  https://doi.org/10.1109/TNNLS.2019.2899262 MathSciNetCrossRefGoogle Scholar
  8. 8.
    L.O. Chua, L. Yang, Cellular neural networks: theory. IEEE Trans. Circuits Syst. 35(10), 1257–1272 (1988)MathSciNetCrossRefGoogle Scholar
  9. 9.
    L.O. Chua, T. Roska, Cellular Neural Networks and Visual Computing: Foundation and Applications (Cambridge University Press, Cambridge, 2005)Google Scholar
  10. 10.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453(7191), 80–83 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    Y.N. Joglekar, S.J. Wolf, The elusive memristor: properties of basic electrical circuits. Eur. J. Phys. 30(4), 661 (2009)Google Scholar
  12. 12.
    R. Stanley Williams, How we found the missing memristor. IEEE Spectr. 45(12), 28–35 (2008)CrossRefGoogle Scholar
  13. 13.
    F. Corinto, A. Ascoli, A boundary condition-based approach to the modeling of memristor nanostructures. IEEE Trans. Circuits Syst. I. Regul. Pap. 59(11), 2713–2726 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    D. Biolek, Z. Biolek, V. Biolkova, Z. Kolka, Reliable modeling of ideal generic memristors via state-space transformation. Radioengineering 24(2), 393–407 (2015)CrossRefGoogle Scholar
  15. 15.
    L.O. Chua, L. Yang, Cellular neural networks: applications. IEEE Trans. Circuits Syst. 35(10), 1273–1290 (1988)MathSciNetCrossRefGoogle Scholar
  16. 16.
    M. Hirsch, Convergent activation dynamics in continuous time networks. Neural Netw. 2, 331–349 (1989)CrossRefGoogle Scholar
  17. 17.
    H.K. Khalil, Nonlinear Systems (Prentice Hall, Upper Saddle River, 2002)Google Scholar
  18. 18.
    J.K. Hale, Ordinary Differential Equations (Wiley Interscience, New York, 1969)zbMATHGoogle Scholar
  19. 19.
    M. Di Marco, M. Forti, L. Pancioni, Complete stability of feedback CNNs with dynamic memristors and second-order cells. Int. J. Circuit Theory Appl. 44, 1959–1981 (2016)CrossRefGoogle Scholar
  20. 20.
    L. Kék, K. Karacs, T. Roska, Cellular wave computing library (templates, algorithms, and programs). Version 2.1, in Research report of Cellular Sensory and Wave Computing Laboratory CSW-1-2007 (2007)Google Scholar
  21. 21.
    M. Di Marco, M. Forti, L. Pancioni, Convergence and multistability of nonsymmetric cellular neural networks with memristors. IEEE Trans. Cybern. 47(10), 2970–2983 (2017)CrossRefGoogle Scholar
  22. 22.
    M. Di Marco, M. Forti, L. Pancioni, New conditions for global asymptotic stability of memristor neural networks. IEEE Trans. Neural Netw. Learn. Syst. 29, 1822–1834 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    M. Di Marco, M. Forti, L. Pancioni, Stability of memristor neural networks with delays operating in the flux-charge domain. J. Franklin Inst. 355(12), 5135–5162 (2018)MathSciNetCrossRefGoogle Scholar
  24. 24.
    R. Tetzlaff, A. Ascoli, I. Messaris, L.O. Chua, Theoretical foundations of memristor cellular nonlinear networks: memcomputing with bistable-like memristors. IEEE Trans. Circuits Syst. I. Regul. Pap. 67(2), 502–515 (2020)MathSciNetCrossRefGoogle Scholar
  25. 25.
    A. Ascoli, I. Messaris, R. Tetzlaff, L.O. Chua, Theoretical foundations of memristor cellular nonlinear networks: stability analysis with dynamic memristors. IEEE Trans. Circuits Syst. I: Regul. Pap. 67(4), 1389–1401 (2020)MathSciNetCrossRefGoogle Scholar
  26. 26.
    A. Ascoli, R. Tetzlaff, S.-M. Kang, L.O. Chua, Theoretical foundations of memristor cellular nonlinear networks: a DRM2-based method to design memcomputers with dynamic memristors. IEEE Trans. Circuits Syst. I: Regul. Pap. 67(8), 2753–2766 (2020).  https://doi.org/10.1109/TCSI.2020.2978460 CrossRefGoogle Scholar
  27. 27.
    Y.V. Pershin, S. La Fontaine, M. Di Ventra, Memristive model of amoeba learning. Phys. Rev. E 80(2), 021926 (2009)Google Scholar
  28. 28.
    T. Roska, L.O. Chua, The CNN universal machine: an analogic array computer. IEEE Trans. Circuits Syst. II. Analog Digit. Signal Process. 40(3):163–173 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2021

Authors and Affiliations

  • Fernando Corinto
    • 1
  • Mauro Forti
    • 2
  • Leon O. Chua
    • 3
  1. 1.Department of Electronics & TelecommunicationsPolitecnico di TorinoTorinoItaly
  2. 2.Department of Information Engineering and MathematicsUniversity of SienaSienaItaly
  3. 3.University of CaliforniaBerkeleyUSA

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