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Handbook of Memristor Networks pp 1289–1361Cite as

Memristor Cellular Automata and Memristor Discrete-Time Cellular Neural Networks

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Abstract

In this paper, we design a cellular automaton and a discrete-time cellular neural network (DTCNN) using nonlinear passive memristors. They can perform a number of applications, such as logical operations, image processing operations, complex behaviors, higher brain functions, etc. By modifying the characteristics of nonlinear memristors, the memristor DTCNN can perform almost all functions of memristor cellular automaton. Furthermore, it can perform more than one function at the same time, that is, it allows multitasking.

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Notes

  1. 1.

    A time-frame is used to identify a start and end of a set of current pulses.

  2. 2.

    All evolution images and processed images in this paper are not obtained by the real memristor cellular automaton circuits, but by computer simulations.

  3. 3.

    Gaussian noise has a probability density function of the normal distribution (Gaussian distribution).

  4. 4.

    We can obtain Eqs. (110) and (111) using the approximation: \(\displaystyle floor \left( \frac{255}{9} |q| \ \right) \approx floor \left( \ 28 \ |q| \ \right) \).

  5. 5.

    10-gradations: \(\{ 0, 28, 56, 84, 112, 140, 168, 196, 224, 252 \}\) levels.

  6. 6.

    During the period \([nT, n T+ \Delta t]\), a positive current read pulse \(I_{p}\) with a height of 1 is applied into the memristor.

  7. 7.

    For more details, see “Bak-Tang-Wiesenfeld sandpile” in Wikipedia, the free encyclopedia.

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Acknowledgements

This work is supported in part by ONR grants No. N00014-07-1-0350 and N00014-09-1-0411.

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Authors and Affiliations

  1. 1-19-20-203, Arae, Jonan-ku, Fukuoka, 814-0101, Japan

    Makoto Itoh

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

    Leon Chua

Authors
  1. Makoto Itoh
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  2. Leon Chua
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Corresponding author

Correspondence to Leon Chua .

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Editors and Affiliations

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

    Leon Chua

  2. Democritus University of Thrace, Xanthi, Greece

    Georgios Ch. Sirakoulis

  3. Department of Computer Science and Creative Technologies, University of the West of England, Bristol, UK

    Andrew Adamatzky

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Itoh, M., Chua, L. (2019). Memristor Cellular Automata and Memristor Discrete-Time Cellular Neural Networks. In: Chua, L., Sirakoulis, G., Adamatzky, A. (eds) Handbook of Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-76375-0_47

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  • DOI: https://doi.org/10.1007/978-3-319-76375-0_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-76374-3

  • Online ISBN: 978-3-319-76375-0

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