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The Fourth Element

  • Leon ChuaEmail author
Chapter

Abstract

This tutorial clarifies the axiomatic definition of \((v^{(\alpha )},i^{(\beta )})\) circuit elements via a look-up-table dubbed an A-pad, of admissible (vi) signals measured via Gedanken Probing Circuits. The \((v^{(\alpha )},i^{(\beta )})\) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element Tour (Nature 453:42–43, 2008 [1]), characterized by a state-dependent Ohm’s law. A logical generalization to memristive devices reveals a common fingerprint consisting of a dense continuum of pinched hysteresis loops whose area decreases with the frequency \(\omega \) and tends to a straight line as \(\omega \rightarrow \infty \), for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used henceforth as a moniker for memristive devices.

References

  1. 1.
    Tour, J.M., He, T.: The fourth element. Nature 453, 42–43 (2008)CrossRefGoogle Scholar
  2. 2.
    Chua, L.O.: Introduction to Nonlinear Network Theory. McGraw Hill Book Co., New York (1969)Google Scholar
  3. 3.
    Chua, L.O.: Device modeling via basic nonlinear circuit elements. IEEE Trans. Circ. Syst. CAS-27, 1014–1044 (1980)Google Scholar
  4. 4.
    Chua, L.O.: Nonlinear circuit foundations for nano devices, Part I: the four-element torus. Proc. IEEE 91, 1830–1859 (2003)CrossRefGoogle Scholar
  5. 5.
    Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circ. Theor. CT-18, 507–519 (1971)CrossRefGoogle Scholar
  6. 6.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  7. 7.
    Chua, L.O.: Introduction to Memristors. IEEE Expert Now Educational Course (2009)Google Scholar
  8. 8.
    Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1723 (2009)CrossRefGoogle Scholar
  9. 9.
    Chua, L.O.: Dynamic nonlinear networks: state of the art. IEEE Trans. Circ. Syst. CAS-27, 1059–1087 (1980)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Biolek, D., Bioleova, V.: Mutator for transforming memristor into memcapacitor. Electron. Lett. 46, 1428–1429 (2010)CrossRefGoogle Scholar
  11. 11.
    Pershin, Y.V., Di Ventra, M.: Teaching memory circuit elements via experiment-based learning, arXiv: 1112.5427v1 [physics.ins-det]
  12. 12.
    Bartle, R.G.: The Elements of Real Analysis, 2nd edn. Wiley, New York (1976)zbMATHGoogle Scholar
  13. 13.
    Chua, L.O.: Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011)CrossRefGoogle Scholar
  14. 14.
    Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64, 209–223 (1976)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Chua, L., Sbitnev, V., Kim, H.: Hodgkin Huxley axon is made of memristors. Int. J. Bifurcat. Chaos 22(3), 1230011 (2012)CrossRefGoogle Scholar
  16. 16.
    Kim, H., Sah, M.P., Adhikari, S.P.: Pinched hysteresis loop is the fingerprint of memristive devices, arXiv:1202.2437v1 [cond-mat.mes-hall]
  17. 17.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to the conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefGoogle Scholar
  18. 18.
    Cole, K.S.: Membranes. Ions and Impulse. University of California Press, Berkeley (1972)Google Scholar
  19. 19.
    Ayrton, H.: The Electric Arc. D. Van Nostrand Co., London (1902)zbMATHGoogle Scholar
  20. 20.
    Prodromakis, T., Toumazou, C., Chua, L.: Two centuries of memristors. Nat. Mater. 11, 478–481 (2012)CrossRefGoogle Scholar
  21. 21.
    Valov, I., Waser, R., Jameson, J.R., Kozicki, M.N.: Electrochemical metallization memories-Fundamentals, applications, prospects. Nanotechnology 2, 254003 (2011)CrossRefGoogle Scholar
  22. 22.
    Bray, M.G., Werner, D.H.: Passive switching of electromagnetic devices with memristors. Appl. Phys. Lett. 96, 0735041–3 (2010)CrossRefGoogle Scholar
  23. 23.
    Borghetti, J., Snider, G.S., Kukes, P.J., Yang, J.J., Stewart, D.R., R.S.: Williams memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010)CrossRefGoogle Scholar
  24. 24.
    Strukov, D.B., Williams, R.S.: Four-dimensional address topology for circuits with stacked multilayer crossbar arrays. Proc. Nat. Acad. Sci. 106, 20155–20158 (2009)CrossRefGoogle Scholar
  25. 25.
    Lehtonen, W., Laiho, M.: Stateful implication logic with memristors. In: Proceedings of IEEE/ACM International Symposium on Architectures, pp. 33–36 (2009)Google Scholar
  26. 26.
    Borghetti, J., Li, Z., Straznicky, X., Li, X., Ohlberg, A., Wu, W., Stewart, D.R., Williams, R.S.: A hybrid nanomemristor/transistor logic circuit capable of self-programming. Proc. Nat. Acad. Sci. 106, 1699–1703 (2009)CrossRefGoogle Scholar
  27. 27.
    Kim, K., Shin, S., Kang, S.-M.: Field programmable stateful logic array. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 30, 1800-1813 (2011)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Linares-Barranco, B., Serrano-Gotarredona, T.: Memristance can explain spike-time-dependent-plasticity in neural synapses. Nature Precedings. hdl:10101/npre. 2009.3010.1 : 31 Mar 2009Google Scholar
  29. 29.
    Jo, S.H., Chang, T., Ebong, I., Bhadviya, B.B., Mazumder, P., Lu, W.: Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010)CrossRefGoogle Scholar
  30. 30.
    Pershin, Y.V., Di Ventra, M.: Neuromorphic, digital and quantum computation with memory circuit elements, arXiv:1009.6025v3 [cond-mat.mes-hall]
  31. 31.
    Snider, G.S.: Spike-timing dependent learning in memristive nanodevices. In: IEEE/ACM International Symposium on Nanoscale Architecture, pp. 85–92 (2008)Google Scholar
  32. 32.
    Liu, T., Kang, Y., Verma, M., Orlowski, M.: Novel highly nonlinear memristive circuit elements for neural networks. In: Proceedings, 2012 IJCNN International Joint Conference on Neural Networks, in Brisbane, Australia (2012). http://doi.org/10.1109/IJCNN.2012.6252460
  33. 33.
    Chang, T., Jo, S.-H., Lu, W.: Short-term memory to long-term memory transition in a nanoscale memristor. Am. Chem. Soc. (ACS) Nano 5, 7669-7676 (2011)CrossRefGoogle Scholar
  34. 34.
    Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurcat. Chaos 18, 3183–3206 (2008)MathSciNetzbMATHGoogle Scholar
  35. 35.
    Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurcat. Chaos 20, 1567–1580 (2010)CrossRefGoogle Scholar
  36. 36.
    Ginoux, J.-M., Letellier, C., Chua, L.O.: Topological analysis of chaotic solution of a three-element memristive circuit. Int. J. Bifurcat. Chaos 20, 3819–3827 (2010)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Itoh, M., Chua, L.O.: Memristor Hamiltonian circuits. Int. J. Bifurcat. Chaos 21, 2395–2425 (2011)CrossRefGoogle Scholar
  38. 38.
    Pham, V.-T., Buscarino, A., Frasca, M., Fortuna, L.: Autowaves in memristive cellular neural networks. Int. J. Bifurcat. Chaos 22, 12300271–9 (2012)CrossRefGoogle Scholar
  39. 39.
    Kim, H., Adhikari, S.P.: Memistor is not memristor, pp. 75–78. Fist Quarter, IEEE Circuits and Systems Magazine (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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