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Memristor Cellular Automata and Memristor Discrete-Time Cellular Neural Networks

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Memristor Networks

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: \(\mathit{floor} ( \frac{255}{9} |q| ) \approx \mathit{floor} ( 28 |q| ) \).

  5. 5.

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

  6. 6.

    During the period [nT,nT+Δt], 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.

References

  1. Chua, L.O.: Memristor—the missing circuit element. IEEE Trans. Circuit Theory CT-18(5), 507–519 (1971)

    Article  Google Scholar 

  2. Chua, L.O.: CNN: A Paradigm for Complexity. World Scientific, Singapore (1998)

    MATH  Google Scholar 

  3. Chua, L.O.: A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science, vols. I–II. World Scientific, Singapore (2006)

    MATH  Google Scholar 

  4. Chua, L.O., Kang, S.M.: Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)

    Article  MathSciNet  Google Scholar 

  5. Chua, L.O., Roska, T.: Cellular Neural Networks and Visual Computing. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  6. Gardner, M.: Mathematical games—the fantastic combinations of John Conway’s new solitaire game “life”. Sci. Am. 223, 120-123 (1970)

    Article  Google Scholar 

  7. Itoh, M., Chua, L.O.: Designing CNN genes. Int. J. Bifurc. Chaos 13(10), 2739–2824 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Itoh, M., Chua, L.O.: Advanced image processing cellular neural networks. Int. J. Bifurc. Chaos 17(4), 1109–1150 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18(11), 3183–3206 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Itoh, M., Chua, L.O.: Imitation of visual illusions via OpenCV and CNN. Int. J. Bifurc. Chaos 18(12), 3551–3609 (2008)

    Article  MathSciNet  Google Scholar 

  11. Itoh, M., Chua, L.O.: Difference equations for cellular automata. Int. J. Bifurc. Chaos 19(3), 805–830 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  12. Johnson, R.C.: Will memristors prove irresistible? EE Times 1538, 30–34 (2008)

    Google Scholar 

  13. Peitgen, H.O., Jurgens, H., Saupe, D.: Chaos and Fractals: New Frontiers of Science. Springer, New York (1992)

    Book  Google Scholar 

  14. Snider, G.S.: Self-organized computation with unreliable, memristive nanodevices. Nanotechnology 18(36), 365202 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

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

Author information

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 Makoto Itoh .

Editor information

Editors and Affiliations

  1. Computer Science Department, University of the West of England, Bristol, United Kingdom

    Andrew Adamatzky

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

    Leon Chua

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Itoh, M., Chua, L. (2014). Memristor Cellular Automata and Memristor Discrete-Time Cellular Neural Networks. In: Adamatzky, A., Chua, L. (eds) Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-02630-5_30

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  • DOI: https://doi.org/10.1007/978-3-319-02630-5_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02629-9

  • Online ISBN: 978-3-319-02630-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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