Abstract
This tutorial clarifies the axiomatic definition of (v (α),i (β)) circuit elements via a look-up-table dubbed an, of admissible (v,i) signals measured via Gedanken Probing Circuits. The (v (α),i (β)) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element (Tour and He in Nature 453:42–43, 2008), 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 ω and tends to a straight line as ω→∞, 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.
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Notes
- 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.
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. (8) represents a summary of the past memory of q(t) measured at t=t 0.
- 3.
References
Tour, J.M., He, T.: The fourth element. Nature 453, 42–43 (2008)
Chua, L.O.: Introduction to Nonlinear Network Theory. McGraw-Hill, New York (1969)
Chua, L.O.: Device modeling via basic nonlinear circuit elements. IEEE Trans. Circuits Syst. CAS-27, 1014–1044 (1980)
Chua, L.O.: Nonlinear circuit foundations for nano devices, Part I: the four-element torus. Proc. IEEE 91, 1830–1859 (2003)
Chua, L.O.: Memristor—the missing circuit element. IEEE Trans. Circuit Theory CT-18, 507–519 (1971)
Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453, 80–83 (2008)
Chua, L.O.: Introduction to memristors. IEEE Expert Now Educational Course (2009)
Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64, 209–223 (1976)
Bartle, R.G.: The Elements of Real Analysis, 2nd edn. Wiley, New York (1976)
Chua, L.O.: Dynamic nonlinear networks: state of the art. IEEE Trans. Circuits Syst. CAS-27, 1059–1087 (1980)
Di Ventra, M., Pershin, Y.V., Chua, L.O.: Circuit elements with memory: memristors, memcapacitors, and meminductors. Proc. IEEE 97, 1717–1723 (2009)
Biolek, D., Bioleova, V.: Mutator for transforming memristor into memcapacitor. Electron. Lett. 46, 1428–1429 (2010)
Pershin, Y.V., Di Ventra, M.: Teaching memory circuit elements via experiment-based learning. arXiv:1112.5427v1 [physics.ins-det]
Chua, L.O.: Resistance switching memories are memristors. Appl. Phys. A 102, 765–783 (2011)
Kim, H., Sah, M.P., Adhikari, S.P.: Pinched hysteresis loop is the fingerprint of memristive devices. arXiv:1202.2437v1 [cond-mat.mes-hall]
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)
Chua, L., Sbitnev, V., Kim, H.: Neurons are poised near the edge of chaos. Int. J. Bifurc. Chaos 22(4), 1250098 (2012)
Cole, K.S.: Membranes, Ions and Impulse. University of California Press, Berkeley (1972)
Ayrton, H.: The Electric Arc. Van Nostrand, London (1902)
Valov, I., Waser, R., Jameson, J.R., Kozicki, M.N.: Electrochemical metallization memories-fundamentals, applications, prospects. Nanotechnology 2, 254003 (2011)
Bray, M.G., Werner, D.H.: Passive switching of electromagnetic devices with memristors. Appl. Phys. Lett. 96, 0735041 (2010)
Borghetti, J., Snider, G.S., Kukes, P.J., Yang, J.J., Stewart, D.R.: Williams memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010)
Strukov, D.B., Williams, R.S.: Four-dimensional address topology for circuits with stacked multilayer crossbar arrays. Proc. Natl. Acad. Sci. USA 106, 20155–20158 (2009)
Lehtonen, W., Laiho, M.: Stateful implication logic with memristors. In: Proc. of IEEE/ACM Int. Symposium on Architectures, pp. 33–36 (2009)
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. Natl. Acad. Sci. USA 106, 1699–1703 (2009)
Kim, K., Shin, S., Kang, S.-M.: Field programmable stateful logic array. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 30, 1800–1813 (2011)
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. 2009
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)
Pershin, Y.V., Di Ventra, M.: Neuromorphic, digital and quantum computation with memory circuit elements. arXiv:1009.6025v3 [cond-mat.mes-hall]
Snider, G.S.: Spike-timing dependent learning in memristive nanodevices. In: IEEE/ACM Int. Symposium on Nanoscale Architecture, pp. 85–92 (2008)
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, Brisbane, Australia, June 2012. doi:10.1109/IJCNN.2012.6252460
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)
Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)
Muthuswamy, B., Chua, L.O.: Simplest chaotic circuit. Int. J. Bifurc. Chaos 20, 1567–1580 (2010)
Ginoux, J.-M., Letellier, C., Chua, L.O.: Topological analysis of chaotic solution of a three-element memristive circuit. Int. J. Bifurc. Chaos 20, 3819–3827 (2010)
Itoh, M., Chua, L.O.: Memristor Hamiltonian circuits. Int. J. Bifurc. Chaos 21, 2395–2425 (2011)
Pham, V.-T., Buscarino, A., Frasca, M., Fortuna, L.: Autowaves in memristive cellular neural networks. Int. J. Bifurc. Chaos 22, 12300271 (2012). 9 pp.
Prodromakis, T., Toumazou, C., Chua, L.: Two centuries of memristors. Nat. Mater. 11, 478–481 (2012)
Chua, L., Sbitnev, V., Kim, H.: Hodgkin Huxley axon is made of memristors. Int. J. Bifurc. Chaos 22(3), 1230011 (2012)
Kim, H., Adhikari, S.P.: Memistor is not memristor. IEEE Circuits Syst. Mag., First Quart. 75–78 (2012)
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Chua, L. (2014). The Fourth Element. In: Adamatzky, A., Chua, L. (eds) Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-02630-5_1
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