Skip to main content
SpringerLink
Log in

If It’s Pinched It’s a Memristor

  • Chapter
  • First Online:
Memristors and Memristive Systems

Abstract

This chapter consists of two parts. Part I gives a circuit-theoretic foundation for the first four elementary nonlinear 2-terminal circuit elements, namely, the resistor, the capacitor, the inductor, and the memristor. Part II consists of a collection of colorful “Vignettes” with carefully articulated text and colorful illustrations of the rudiments of the memristor and its characteristic fingerprints and signatures. It is intended as a self-contained pedagogical primer for beginners who have not heard of memristors before.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Observe that the voltage v and the current i are defined axiomatically via two instruments called voltmeter and ammeter, without invoking any physical concepts such as electric field, magnetic field, charge, flux linkages, etc. One does not even have to know how a voltmeter, or an ammeter, works. They are just names assigned to the instruments.

  2. 2.

    In practice one can never know the precise signal i(t) over the infinite past. Rather we can only set up our measurements to begin at some initial time t = t 0. Consequently, the initial condition q 0 in Eq. (2.8) represents a summary of the past memory of q(t) measured at t = t 0.

  3. 3.

    Hodgkin and Huxley were awarded the 1965 Nobel Prize in physiology for their derivation of the circuit shown in Fig. 2.4a, where the two memristors were drawn as time-varying resistors in Fig. 1 (page 501) of [16].

References

  1. J.M. Tour, T. He, The fourth element. Nature 453, 42–43 (1 May 2008)

    Google Scholar 

  2. L.O. Chua, Introduction to Nonlinear Network Theory (McGraw Hill Book Co., New York, 1969)

    Google Scholar 

  3. L.O. Chua, Device modeling via basic nonlinear circuit elements. IEEE Trans. Circuit Syst. 27, 1014–1044 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. L.O. Chua, Nonlinear circuit foundations for nano devices, Part I: The four-element torus. Proc. IEEE 91, 1830–1859 (2003)

    Google Scholar 

  5. L.O. Chua, Memristor: The missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)

    Article  Google Scholar 

  6. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453, 80–83 (2008)

    Article  Google Scholar 

  7. L.O. Chua, Introduction to memristors. IEEE Expert Now, Educational Course, 2009

    Google Scholar 

  8. M. Di Ventra, Y.V. Pershin, L.O. Chua, Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1723 (2009)

    Article  Google Scholar 

  9. L.O. Chua, L.O.: Dynamic nonlinear networks: State of the art. IEEE Trans. Circuits Syst. 27, 1059–1087 (1980)

    Google Scholar 

  10. D. Biolek, V. Bioleova, Mutator for transforming memristor into memcapacitor. Electron. Lett. 46, 1428–1429 (2010)

    Article  Google Scholar 

  11. Y.V. Pershin, M. Di Ventra, Teaching memory circuit elements via experiment-based learning. arXiv: 1112.5427v1 [physics.ins-det]

    Google Scholar 

  12. R.G. Bartle, The Elements of Real Analysis, 2nd edn. (Wiley, New York, 1976)

    MATH  Google Scholar 

  13. L.O. Chua, Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011)

    Article  Google Scholar 

  14. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64, 209–223 (1976)

    Article  MathSciNet  Google Scholar 

  15. H. Kim, M.P. Sah, S.P. Adhikari, Pinched hysteresis loop is the fingerprint of memristive devices. arXiv:1202.2437v1 [cond-mat.mes-hall]

    Google Scholar 

  16. A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to the conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)

    Google Scholar 

  17. K.S. Cole, Membranes, Ions and Impulse (University of California Press, Berkeley, 1972)

    Google Scholar 

  18. L. Chua, V. Sbitnev, H. Kim, Hodgkin Huxley axon is made of memristors. Int. J. Bifurcat. Chaos 22(3), 1230011 (2012)

    Article  Google Scholar 

  19. H. Ayrton, The Electric Arc (D.Van Nostrand Co., London, 1902)

    Google Scholar 

  20. T. Prodromakis, C. Toumazou, L. Chua, Two centuries of memristors. Nat. Mater. 11, 478–481 (June 2012)

    Article  Google Scholar 

  21. I. Valov, R. Waser, J.R. Jameson, M.N. Kozicki, Electrochemical metallization memories: Fundamentals, applications, prospects. Nanotechnol. 2, 254003 (2011)

    Article  Google Scholar 

  22. M.G. Bray, D.H. Werner, Passive switching of electromagnetic devices with memristors. Appl. Phys. Lett. 96, 0735041-3 (2010)

    Google Scholar 

  23. J. Borghetti, G.S. Snider, P.J. Kukes, J.J. Yang, D.R. Stewart, R.S. Williams, Williams memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010)

    Article  Google Scholar 

  24. D.B. Strukov, R.S. Williams, Four-dimensional address topology for circuits with stacked multilayer crossbar arrays. Proc. Natl. Acad. Sci. 106, 20155–20158 (2009)

    Article  Google Scholar 

  25. W. Lehtonen, M. Laiho, Stateful implication logic with memristors. Proc. IEEE/ACM International Symposium on Architectures, pp. 33–36, San Francisco, CA 2009

    Google Scholar 

  26. J. Borghetti, Z. Li, X. Straznicky, X. Li, A. Ohlberg, W. Wu, D.R. Stewart, R.S. Williams, A hybrid nanomemristor/transistor logic circuit capable of self-programming. Proc. Natl. Acad. Sci. 106, 1699–1703 (2009)

    Article  Google Scholar 

  27. K. Kim, S. Shin, S.-M. Kang, Field programmable stateful logic array. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 30, 1800–1813 (2011)

    Article  Google Scholar 

  28. B. Linares-Barranco, T. Serrano-Gotarredona, Memristance can explain spike-time-dependent-plasticity in neural synapses. Nature Precedings, hdl:10101/npre. 2009.3010.1: 31 March 2009

    Google Scholar 

  29. S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P.Lu.W. Mazumder, Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301

    Google Scholar 

  30. Pershin, Y.V., Di Ventra, M.: Neuromorphic, digital and quantum computation with memory circuit elements. arXiv:1009.6025v3 [cond-mat.mes-hall]

    Google Scholar 

  31. G.S. Snider, Spike-timing dependent learning in memristive nanodevices, IEEE/ACM International Symposium on Nanoscale Architecture, Anaheim, CA, 85–92, 2008

    Google Scholar 

  32. T. Liu, Y. Kang, M. Verma, M. Orlowski, Novel Highly Nonlinear Memristive Circuit Elements for Neural Networks. Proceedings, 2012 IJCNN International Joint Conference on Neural Networks, in Brisbane, Australia, June 2012, doi 10.1109/IJCNN.2012.6252460

    Google Scholar 

  33. T. Chang, S.-H. Jo, W. Lu, Short-term memory to long-term memory transition in a nanoscale memristor. Am. Chem. Soc. (ACS) Nano 5, 7669–7676 (2011)

    Google Scholar 

  34. M. Itoh, L.O. Chua, Memristor oscillators. Int. J. Bifurcat. Chaos 18, 3183–3206 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. B. Muthuswamy, L.O. Chua, Simplest chaotic circuit. Int. J. Bifurcat. Chaos 20, 1567–1580 (2010)

    Article  Google Scholar 

  36. J.-M. Ginoux, C. Letellier, L.O. Chua, Topological analysis of chaotic solution of a three-element memristive circuit. Int. J. Bifurcat. Chaos 20, 3819–3827 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Itoh, L.O. Chua, Memristor Hamiltonian circuits. Int. J. Bifurcat. Chaos 21, 2395–2425 (2011)

    Article  MATH  Google Scholar 

  38. V.-T. Pham, A. Buscarino, M. Frasca, L. Fortuna, Autowaves in memristive cellular neural networks. Int. J. Bifurcat. Chaos 22, 12300271-9 (2012)

    Google Scholar 

  39. L. Chua, V. Sbitnev, H. Kim, Neurons are poised near the edge of chaos. Int. J. Bifurcat. Chaos 22(4), 1250098 (2012)

    Article  Google Scholar 

  40. H. Kim, S.P. Adhikari, Memistor is mot memristor. IEEE Circuits and Systems Magazine, Fist Quarter 2012, pp. 75–78

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94720, USA

    Leon Chua

Authors
  1. Leon Chua
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leon Chua .

Editor information

Editors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universität Dresden, Dresden, Germany

    Ronald Tetzlaff

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chua, L. (2014). If It’s Pinched It’s a Memristor. In: Tetzlaff, R. (eds) Memristors and Memristive Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9068-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-9068-5_2

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-9067-8

  • Online ISBN: 978-1-4614-9068-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation