Skip to main content

Bio-inspired Neural Networks

  • Chapter
Memristor Networks

Abstract

We describe a biological network and the principal mechanisms that are responsible for learning and memory. We start with a description of the morphology of these networks and their components, such as neurons and synapses. Then, we will identify crucial components of the information processing, such as ion flux and the induced mechanisms, e.g., long-term potentiation and depression. Next, we will compare the behaviour of a memristive system with the mechanisms identified in biological systems and present corresponding experiments and a few simulations. Finally, we will present more abstract ways of using memristors to solve complex problems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

References

  1. Afifi, A., Ayatollahi, A., Raissi, F.: STDP implementation using memristive nanodevice in CMOS-nano neuromorphic networks. IEICE Electron. Express 6(3), 148–153 (2009)

    Article  Google Scholar 

  2. Andersen, P., Sundberg, S., Sveen, O., Wigström, H.: Specific long-lasting potentiation of synaptic transmission in hippocampal slices. Nature 266(5604), 736–737 (1977)

    Article  Google Scholar 

  3. Aur, D., Jog, M., Poznanski, R.R.: Computing by physical interaction in neurons. J. Integr. Neurosci. 10(04), 413–422 (2011)

    Article  Google Scholar 

  4. Aziz, P., Sorensen, H., van der Spiegel, J.: An overview of sigma-delta converters. IEEE Signal Process. Mag. 13(1), 61–84 (1996)

    Article  Google Scholar 

  5. Barrionuevo, G., Brown, T.: Associative long-term potentiation in hippocampal slices. Proc. Natl. Acad. Sci. USA 80(23), 7347–7351 (1983)

    Article  Google Scholar 

  6. Bi, G.q., Poo, M.m.: Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neurosci. 18(24), 10464–10472 (1998)

    Google Scholar 

  7. Bliss, T., Collingridge, G.: A synaptic model of memory—long-term potentiation in the hippocampus. Nature 361(6407), 31–39 (1993)

    Article  Google Scholar 

  8. Bliss, T., Gardner-Medwin, A.R.: Long-lasting potentiation of synaptic transmission in dentate area of unanesthetized rabbit following stimulation of perforant path. J. Physiol., Lond. 232(2), 357–374 (1973)

    Google Scholar 

  9. Bliss, T., Lømo, T.: Long-lasting potentiation of synaptic transmission in dentate area of anesthetized rabbit following stimulation of perforant path. J. Physiol., Lond. 232(2), 331–356 (1973)

    Google Scholar 

  10. Borghetti, J., Li, Z., Straznicky, J., Li, X., Ohlberg, D.A.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(6), 1699–1703 (2009)

    Article  Google Scholar 

  11. Borghetti, J., Snider, G.S., Kuekes, P.J., Yang, J.J., Stewart, D.R., Williams, R.S.: ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464(7290), 873–876 (2010)

    Article  Google Scholar 

  12. Cajal, S.R.: Histology of the Nervous System of Man and Vertebrates. Oxford University Press, London (1995)

    Google Scholar 

  13. Cantley, K.D., Subramaniam, A., Stiegler, H.J., Chapman, R.A., Vogel, E.M.: Neural learning circuits utilizing nano-crystalline silicon transistors and memristors. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 565–573 (2012)

    Article  Google Scholar 

  14. Carpenter, G., Milenova, B., Noeske, B.: Distributed ARTMAP: a neural network for fast distributed supervised learning. Neural Netw. 11(5), 793–813 (1998)

    Article  Google Scholar 

  15. Cassenaer, S., Laurent, G.: Hebbian STDP in mushroom bodies facilitates the synchronous flow of olfactory information in locusts. Nature 448(7154), 709–712 (2007)

    Article  Google Scholar 

  16. Chang, T., Jo, S.H., Kim, K.H., Sheridan, P., Gaba, S., Lu, W.: Synaptic behaviors and modeling of a metal oxide memristive device. Appl. Phys. A 102(4), 857–863 (2011)

    Article  Google Scholar 

  17. Chen, X., Wu, G., Dinghua, B.: Resistive switching behavior of Pt/Mg0.2Zn0.8O/Pt devices for nonvolatile memory applications. Appl. Phys. Lett. 93, 093501 (2008)

    Article  Google Scholar 

  18. Choi, S.J., Kim, G.B., Lee, K., Kim, K.H., Yang, W.Y., Cho, S., Bae, H.J., Seo, D.S., Kim, S.I., Lee, K.J.: Synaptic behaviors of a single metal–oxide–metal resistive device. Appl. Phys. A 102(4), 1019–1025 (2011)

    Article  Google Scholar 

  19. Chua, L.O.: Introduction to Nonlinear Network Theory. McGraw-Hill, New York (1969)

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Chua, L.O., Desoer, C.A., Kuh, E.S.: Linear and Nonlinear Circuits. McGraw-Hill, New York (1987)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Cole, K.: Rectification and inductance in the squid giant axon. J. Gen. Physiol. 25(1), 29–51 (1941)

    Article  Google Scholar 

  26. Cole, K.: Membranes, Ions and Impulses. University of California Press, Berkeley (1972)

    Google Scholar 

  27. Cole, K., Baker, R.: Longitudinal impedance of the squid giant axon. J. Gen. Physiol. 24(6), 771–788 (1941)

    Article  Google Scholar 

  28. Doyere, V., Laroche, S.: Linear relationship between the maintenance of hippocampal long-term potentiation and retention of an associative memory. Hippocampus 2(1), 39–48 (1992)

    Article  Google Scholar 

  29. Eccles, J.: The Ferrier lecture: the nature of central inhibition. Proc. R. Soc. Lond. B, Biol. Sci. 153, 445–476 (1961)

    Article  Google Scholar 

  30. Eccles, J., McIntyre, A.: Plasticity of mammalian monosynaptic reflexes. Nature 167(4247), 466–468 (1951)

    Article  Google Scholar 

  31. Fusi, S., Abbott, L.F.: Limits on the memory storage capacity of bounded synapses. Nat. Neurosci. 10(4), 485–493 (2007)

    Google Scholar 

  32. Ge, Y., Dong, Z., Bagot, R.C., Howland, J.G., Phillips, A.G., Wong, T.P., Wang, Y.T.: Hippocampal long-term depression is required for the consolidation of spatial memory. Proc. Natl. Acad. Sci. USA 107(38), 16697–16702 (2010)

    Article  Google Scholar 

  33. Goda, Y., Stevens, C.: Long-term depression properties in a simple system. Neuron 16, 103–111 (1996)

    Article  Google Scholar 

  34. Hodgkin, A., Huxley, A.: Action potentials recorded from inside a nerve fibre. Nature 144, 710–711 (1939)

    Article  Google Scholar 

  35. Hodgkin, A., Huxley, A.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., Lond. 117(4), 500–544 (1952)

    Google Scholar 

  36. Imielski, Y., Schwamborn, J.C., Lüningschrör, P., Heimann, P., Holzberg, M., Werner, H., Leske, O., Püschel, A.W., Memet, S., Heumann, R., Israel, A., Kaltschmidt, C., Kaltschmidt, B.: Regrowing the adult brain: NF-κB controls functional circuit formation and tissue homeostasis in the dentate gyrus. PLoS ONE 7(2), e30838 (2012)

    Article  Google Scholar 

  37. Indiveri, G., Chicca, E., Douglas, R.: A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity. IEEE Trans. Neural Netw. 17(1), 211–221 (2006)

    Article  Google Scholar 

  38. Indiveri, G., Stefanini, F., Chicca, E.: Spike-based learning with a generalized integrate and fire silicon neuron. In: 2010 IEEE International Symposium on Circuits and Systems, pp. 1951–1954 (2010)

    Chapter  Google Scholar 

  39. Jack, J.J.B., Noble, D., Tsien, R.W.: Electric current flow in excitable cells. OUP Australia and New Zealand (1975)

    Google Scholar 

  40. 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(4), 1297–1301 (2010)

    Article  Google Scholar 

  41. Kaltschmidt, B., Kaltschmidt, C.: NF-κB in the nervous system. Cold Spring Harb. Perspect. Biol. 1(3), a001271 (2009)

    Google Scholar 

  42. Knight, B.: Dynamics of encoding in a population of neurons. J. Gen. Physiol. 59(6), 734 (1972)

    Article  Google Scholar 

  43. Koch, C.: Biophysics of Computation. Oxford University Press, London (1999)

    Google Scholar 

  44. Konorski, J.: Conditioned Reflexes and Neuron Organization. Cambridge University Press, Cambridge (1948)

    Google Scholar 

  45. Krzysteczko, P., Kou, X., Rott, K., Thomas, A.: Current induced resistance change of magnetic tunnel junctions with ultra-thin MgO tunnel barriers. J. Magn. Magn. Mater. 321, 144 (2008)

    Article  Google Scholar 

  46. Krzysteczko, P., Reiss, G., Thomas, A.: Memristive switching of MgO based magnetic tunnel junctions. Appl. Phys. Lett. 95(11), 112508 (2009)

    Article  Google Scholar 

  47. Krzysteczko, P., Münchenberger, J., Schäfers, M., Reiss, G., Thomas, A.: The memristive magnetic tunnel junction as a nanoscopic synapse-neuron system. Adv. Mater. 24, 762–766 (2012)

    Article  Google Scholar 

  48. Lapicque, L.: Lapicque: recherches quantitatives sur l’excitation des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gén. 9 (1907)

    Google Scholar 

  49. Lapicque, L.: L’excitabilité en fonction du temps. Presses Universitaires de France, Paris (1926)

    Google Scholar 

  50. Lee, M.J., Lee, C.B., Lee, D., Lee, S.R., Chang, M., Hur, J.H., Kim, Y.B., Kim, C.J., Seo, D.H., Seo, S., Chung, U.I., Yoo, I.K., Kim, K.: A fast, high-endurance and scalable non-volatile memory device made from asymmetric Ta2O5−x /TaO2−x bilayer structures. Nat. Mater. 10(8), 625–630 (2011)

    Article  Google Scholar 

  51. Levy, W., Steward, O.: Synapses as associative memory elements in the hippocampal-formation. Brain Res. 175(2), 233–245 (1979)

    Article  Google Scholar 

  52. Linn, E., Rosezin, R., Kuegeler, C., Waser, R.: Complementary resistive switches for passive nanocrossbar memories. Nat. Mater. 9(5), 403–406 (2010)

    Article  Google Scholar 

  53. Luscher, C., Malenka, R.C.: NMDA receptor-dependent long-term potentiation and long-term depression (LTP/LTD). Cold Spring Harbor Perspectives in Biology 4(6), a005710 (2012)

    Article  Google Scholar 

  54. Lynch, G., Dunwiddie, T., Gribkoff, V.: Heterosynaptic depression—postsynaptic correlate of long-term potentiation. Nature 266(5604), 737–739 (1977)

    Article  Google Scholar 

  55. Maekawa, S., Shinjo, T. (eds.): Spin Dependent Transport in Magnetic Nanostructures. Advances in Condensed Matter Science. CRC Press, Boca Raton (2002)

    Google Scholar 

  56. Malenka, R.: Postsynaptic factors control the duration of synaptic enhancement in area Ca1 of the hippocampus. Neuron 6(1), 53–60 (1991)

    Article  Google Scholar 

  57. Manahan-Vaughan, D., Braunewell, K.: Novelty acquisition is associated with induction of hippocampal long-term depression. Proc. Natl. Acad. Sci. USA 96(15), 8739–8744 (1999)

    Article  Google Scholar 

  58. Mauro, A.: Anomalous impedance, a phenomenological property of time-variant resistance—an analytic review. Biophys. J. 1(4), 353–372 (1961)

    Article  Google Scholar 

  59. Mayford, M., Siegelbaum, S.A., Kandel, E.R.: Synapses and memory storage. Cold Spring Harbor Perspectives in Biology 4(6), a005751 (2012)

    Article  Google Scholar 

  60. McNaughton, B., Douglas, R., Goddardd, G.: Synaptic enhancement in fascia dentata—cooperativity among coactive afferents. Brain Res. 157(2), 277–293 (1978)

    Article  Google Scholar 

  61. Mead, C.: Neuromorphic electronic systems. Proc. IEEE 78(10), 1629–1636 (1990)

    Article  Google Scholar 

  62. Moodera, J., Mathon, G.: Spin polarized tunneling in ferromagnetic junctions. J. Magn. Magn. Mater. 200(1–3), 248–273 (1999)

    Article  Google Scholar 

  63. Morris, R., Davis, S., Butcher, S.: Hippocampal synaptic plasticity and NMDA receptors—a role in information-storage. Philos. Trans. R. Soc. B 329(1253), 187–204 (1990)

    Article  Google Scholar 

  64. Muenchenberger, J., Krzysteczko, P., Reiss, G., Thomas, A.: Improved reliability of magnetic field programmable gate arrays through the use of memristive tunnel junctions. J. Appl. Phys. 110(9), 096105 (2011)

    Article  Google Scholar 

  65. Nakagaki, T., Yamada, H., Toth, A.: Maze-solving by an amoeboid organism. Nature 407(6803), 470 (2000)

    Article  Google Scholar 

  66. Neftci, E., Chicca, E., Indiveri, G., Douglas, R.: A systematic method for configuring VLSI networks of spiking neurons. Neural Comput. 23, 2457–2497 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  67. Norrby, E.: Nobel Prizes. World Scientific, Singapore (2010)

    Book  Google Scholar 

  68. Pavlov, I.: Conditioned Reflexes: An Investigation of the Physiological Activity of the Cerebral Cortex. Oxford University Press, London (1927)

    Google Scholar 

  69. Pershin, Y.V., Di Ventra, M.: Experimental demonstration of associative memory with memristive neural networks. Neural Netw. 23(7), 881–886 (2010)

    Article  Google Scholar 

  70. Pershin, Y.V., Di Ventra, M.: Neuromorphic, digital, and quantum computation with memory circuit elements. Proc. IEEE 100(6), 2071–2080 (2010)

    Article  Google Scholar 

  71. Pershin, Y.V., Di Ventra, M.: Solving mazes with memristors: a massively parallel approach. Phys. Rev. E 84(4), 046703 (2011)

    Article  Google Scholar 

  72. Pershin, Y., La Fontaine, S., Di Ventra, M.: Memristive model of amoeba learning. Phys. Rev. E 80(2), 021926 (2009)

    Article  Google Scholar 

  73. Poon, C.S.: Neuromorphic silicon neurons and large-scale neural networks: challenges and opportunities. Front. Neurosci. 1–3 (2011)

    Google Scholar 

  74. Rubin, D., Wenzel, A.: One hundred years of forgetting: a quantitative description of retention. Psychol. Rev. 103(4), 734–760 (1996)

    Article  Google Scholar 

  75. Rubin, D., Hinton, S., Wenzel, A.: The precise time course of retention. J. Exp. Psychol. Learn. 25(5), 1161–1176 (1999)

    Article  Google Scholar 

  76. Sbiaa, R., Meng, H., Piramanayagam, S.N.: Materials with perpendicular magnetic anisotropy for magnetic random access memory. Phys. Status Solidi RRL 5(12), 413–419 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  78. Snider, G.: Spike-timing-dependent learning in memristive nanodevices. Nanoscale Archit. 85–92 (2008)

    Google Scholar 

  79. Stein, R.: Frequency of nerve action potentials generated by applied currents. Proc. R. Soc. Lond. B, Biol. Sci. 167(1006), 64 (1967)

    Article  Google Scholar 

  80. Strübing, C., Ahnert-Hilger, G., Shan, J., Wiedenmann, B., Hescheler, J., Wobus, A.M.: Differentiation of pluripotent embryonic stem cells into the neuronal lineage in vitro gives rise to mature inhibitory and excitatory neurons. Mech. Dev. 53, 275–287 (1995)

    Article  Google Scholar 

  81. Thomas, A.: Memristor-based neural networks. J. Phys. D, Appl. Phys. 46(9), 093001 (2013)

    Article  Google Scholar 

  82. Tuckwell, H.C.: Introduction to Theoretical Neurobiology. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  83. Turel, O., Lee, J., Ma, X., Likharev, K.: Neuromorphic architectures for nanoelectronic circuits. Int. J. Circuit Theory Appl. 32(5), 277–302 (2004)

    Article  Google Scholar 

  84. Van Essen, D.C., Ugurbil, K., Auerbach, E., Barch, D., Behrens, T.E.J., Bucholz, R., Chang, A., Chen, L., Corbetta, M., Curtiss, S.W., Della Penna, S., Feinberg, D., Glasser, M.F., Harel, N., Heath, A.C., Larson-Prior, L., Marcus, D., Michalareas, G., Moeller, S., Oostenveld, R., Petersen, S.E., Prior, F., Schlaggar, B.L., Smith, S.M., Snyder, A.Z., Xu, J., Yacoub, E., Consortium, W.M.H.: The human connectome project: a data acquisition perspective. NeuroImage 62(4), 2222–2231 (2012)

    Article  Google Scholar 

  85. von Neumann, J.: First draft of a report on the EDVAC. Tech. rep., University of Pennsylvania (1945)

    Google Scholar 

  86. Wong, P., Gray, R.: Sigma-delta modulation with I.I.D. Gaussian inputs. IEEE Trans. Inf. Theory 36(4), 784–798 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  87. Wrona, J., Langer, J., Ocker, B., Maass, W., Kanak, J., Stobiecki, T., Powroźnik, W.: Low resistance magnetic tunnel junctions with MgO wedge barrier. J. Phys. Conf. Ser. 200(5), 052032 (2010)

    Article  Google Scholar 

  88. Xia, Q., Robinett, W., Cumbie, M.W., Banerjee, N., Cardinali, T.J., Yang, J.J., Wu, W., Li, X., Tong, W.M., Strukov, D.B., Snider, G.S., Medeiros-Ribeiro, G., Williams, R.S.: Memristor-CMOS hybrid integrated circuits for reconfigurable logic. Nano Lett. 9(10), 3640–3645 (2009)

    Article  Google Scholar 

  89. Yan, H., Choe, H., Nam, S., Hu, Y., Das, S.: Programmable nanowire circuits for nanoprocessors. Nature 470, 240–244 (2011)

    Article  Google Scholar 

  90. Young, J.: The structure of nerve fibres in cephalopods and crustacea. Proc. R. Soc. Lond. B, Biol. Sci. 121(822), 319–337 (1936)

    Article  Google Scholar 

  91. Ziegler, M., Soni, R., Patelczyk, T., Ignatov, M., Bartsch, T., Meuffels, P., Kohlstedt, H.: An electronic version of Pavlov’s dog. Adv. Funct. Mater. 22(13), 2744–2749 (2012)

    Article  Google Scholar 

  92. Zuse, K.: Der Computer—Mein Lebenswerk: 100 Jahre Zuse. Springer, Berlin (2010)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank Barbara Kaltschmidt and Elisabetta Chicca for many helpful discussions. Furthermore, we are grateful to Patryk Krzysteczko, Jana Münchenberger, Stefan Niehörster, Matthias Schürmann, Marius Schirmer, Olga Simon, Savio Fabretti, and Joachim Sterz. Additionally, we would like to thank Günter Reiss and Andreas Hütten for the continuous support of our work. The Ministry of Innovation, Science and Research (MIWF) of North Rhine-Westfalia funded this research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andy Thomas .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Thomas, A., Kaltschmidt, C. (2014). Bio-inspired Neural Networks. In: Adamatzky, A., Chua, L. (eds) Memristor Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-02630-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02630-5_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02629-9

  • Online ISBN: 978-3-319-02630-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics