Skip to main content

Dynamics of Biomimetic Electronic Artificial Neural Networks

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 6))

Abstract

We explore the key aspects of the dynamics of small networks of biomimetic artificial electronic neurons, including the role of local dynamics, network topology and noise. Models include Keener’s and Maeda and Makino’s “minimal” model circuits for FitzHugh-Nagumo neurons as well as the Belousov-Zhabotinsky chemical reaction, the prototype chemical oscillatory system. A wide variety of complex synchronization and emergent behavior is seen. There are potential applications to computer science, biology, and biomedicine.

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

Buying options

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
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. E.M.E. Arumugam, M.L. Spano, A chimeric path to neuronal synchronization. Chaos 25, 013107 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Belair, L. Glass, U. an der Heiden, J. Milton, Dynamical disease: identification, temporal aspects and treatment strategies of human illness. Chaos 5(1), 1–7 (1995)

    Google Scholar 

  3. B.P. Belousov, A periodic reaction and its mechanism. Compilation of Abstracts on Radiation Medicine 147(145), 1 (1959)

    Google Scholar 

  4. A. Beuter, J. Bélair, C. Labrie, Feedback and delays in neurological diseases: a modeling study using dynamical systems. Bull. Math. Biol. 55, 525–541 (1993)

    MATH  Google Scholar 

  5. S.L. Bressler, V. Menon, Large-scale brain networks in cognition: emerging methods and principles. Trends Cognitive Sci. 14(6), 277–290 (2010)

    Article  Google Scholar 

  6. A. Bulsara, E.W. Jacobs, T. Zhou, F. Moss, L. Kiss, Stochastic resonance in a single neuron model: Theory and analog simulation. J. Theoret. Biol. 152, 531–555 (1991)

    Article  Google Scholar 

  7. L. Chua, Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. M. Conrad, H.M. Hastings, Scale change and the emergence of information processing primitives. J. Theoret. Biol. 112(4), 741–755 (1985)

    Article  MathSciNet  Google Scholar 

  10. R. Douglas, M. Mahowald, C. Mead, Neuromorphic analogue VLSI. Ann. Rev. Neurosci. 18, 255–281 (1995)

    Article  Google Scholar 

  11. D.S. Echt, P.R. Liebson, L.B. Mitchell, R.W. Peters, D. Obias-Manno, A.H. Barker, D. Arensberg, A. Baker, L. Friedman, H.L. Greene, M.L. Huther, Mortality and morbidity in patients receiving encainide, flecainide, or placebo: the Cardiac Arrhythmia Suppression Trial. New Engl. J. Med. 324(12), 781–788 (1991)

    Article  Google Scholar 

  12. I.R. Epstein, J.A. Pojman, An Introduction to Nonlinear Chemical Dynamics (Oxford University Press, New York, 1998)

    Google Scholar 

  13. G.B. Ermentrout, http://www.math.pitt.edu/~bard/classes/wppdoc/readme.htm. Accessed 24 Aug 2016

  14. G.B. Ermentrout, D.H. Terman, Mathematical Foundations of Neuroscience (Springer Science and Business Media, New York, 2010)

    Book  MATH  Google Scholar 

  15. R.J. Field, Chaos in the Belousov-Zhabotinsky reaction. Mod. Phys. Lett. B 29, 1530015 (2015)

    Article  Google Scholar 

  16. R.J. Field, E. Körös, R.M. Noyes, Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94, 8649–8664 (1972)

    Article  Google Scholar 

  17. R.J. Field, R.M. Noyes, Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Chem. Phys. 60, 1877–1884 (1974)

    Article  Google Scholar 

  18. R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445–466 (1961)

    Article  Google Scholar 

  19. P. Foerster, S.C. Müller, B. Hess, Critical size and curvature of wave formation in an excitable chemical medium. Proc. National Acad. Sci. USA 86, 6831–6834 (1989)

    Article  Google Scholar 

  20. A. Garfinkel, P.S. Chen, D.O. Walter, H.S. Karagueuzian, B. Kogan, S.J. Evans, M. Karpoukhin, C. Hwang, T. Uchida, M. Gotoh, O. Nwasokwa, Quasiperiodicity and chaos in cardiac fibrillation. J. Clin. Invest. 99(2), 305–314 (1997)

    Article  Google Scholar 

  21. W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition (Cambridge University. Press., Cambridge UK 2014), http://neuronaldynamics.epfl.ch/online/index.html. Accessed 24 Aug 2016

  22. L. Glass, M.C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton NJ, 1988)

    MATH  Google Scholar 

  23. B.J. Gluckman, T.I. Netoff, E.J. Neel, W.L. Ditto, M.L. Spano, S.J. Schiff, Stochastic resonance in a neuronal network from mammalian brain. Phys. Rev. Lett. 77, 4098–4101 (1996)

    Article  Google Scholar 

  24. H.M. Hastings, R.J. Field, S.G. Sobel, Microscopic fluctuations and pattern formation in a supercritical oscillatory chemical system. J. Chem. Phys. 119(6), 3291–3296 (2003)

    Article  Google Scholar 

  25. H.M. Hastings, S.G. Sobel, R.J. Field, D. Bongiovi, B. Burke, D. Richford, K. Finzel, M. Garuthara, Bromide control, bifurcation and activation in the Belousov-Zhabotinsky Reaction. J. Phys. Chem. A 112, 4715–4718 (2008)

    Article  Google Scholar 

  26. E.M. Izhikevitch, Dynamical systems in neuroscience: the geometry of excitability and bursting (MIT Press, Cambridge MA, 2007)

    Google Scholar 

  27. E.M. Izhikevich, R. FitzHugh, Fitzhugh-Nagumo model. Scholarpedia 1(9), 1349 (2006)

    Article  Google Scholar 

  28. A.L. Kawczyński, B. Nowakowski, Master equation simulations of a model of a thermochemical system. Phys. Rev. E 68, 036218 (2003)

    Article  Google Scholar 

  29. J.P. Keener, Analog circuitry for the van der Pol and FitzHugh-Nagumo equations.”. IEEE Trans. Systems Man Cybernetics 5, 1010–1014 (1983)

    Article  Google Scholar 

  30. W. Klimesch, An algorithm for the EEG frequency architecture of consciousness and brain body coupling. Frontiers Human Neurosci. 7 (2013). doi:10.3389/fnhum.2013.00766

  31. B. Land, X. Shen (2013), https://people.ece.cornell.edu/land/courses/ece1810/LTspice/. Accessed 24 Aug 2016

  32. B. Land, X. Shen (2013), https://people.ece.cornell.edu/land/PROJECTS/NeuralModels/index.html. Accessed 24 Aug 2016

  33. N. Li, J. Delgado, H.O. González-Ochoa, I.R. Epstein, S. Fraden, Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets. Phys. Chem. Chem. Phys. 16, 10965–10978 (2014)

    Article  Google Scholar 

  34. Y. Maeda, H. Makino, A pulse-type hardware neuron model with beating, bursting excitation and plateau potential. BioSystems 58, 93–100 (2000)

    Article  Google Scholar 

  35. B. McNamara, K. Wiesenfeld, Theory of stochastic resonance. Phys. Rev. A 39, 4854 (1989)

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. C.A. Mead, M.A. Mahowald, A silicon model of early visual processing. Neural Netw. 1, 91–97 (1988)

    Article  Google Scholar 

  38. J. Murray, http://johndmurray.org/teaching/. Accessed 24 Aug 2016

  39. J. Nagumo, S. Arimoto, S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proc. IRE 50, 2061–2070 (1962)

    Article  Google Scholar 

  40. D.L. Packer, T.M. Munger, S.B. Johnson, K.T. Cragun, Mechanism of lethal proarrhythmia observed in the Cardiac Arrhythmia Suppression Trial: role of adrenergic modulation of drug binding. Pacing Clin. Electrophysiol. 20(2), 455–467 (1997)

    Article  Google Scholar 

  41. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: a Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge UK, 2001)

    Book  MATH  Google Scholar 

  42. C.M. Pratt, L.A. Moyé, The Cardiac Arrhythmia Suppression Trial. Circulation 91, 245 (1995)

    Article  Google Scholar 

  43. D.M. Roden, Ionic mechanisms for prolongation of refractoriness and their proarrhythmic and antiarrhythmic correlates. Amer. J. Cardiology 78, 12–16 (1966)

    Article  Google Scholar 

  44. C. Rouvas-Nicolis, G. Nicolis, Stochast. Reson. Scholarpedia 2(11), 1474 (2007)

    Article  Google Scholar 

  45. S.K. Scott, Oscillations, Waves and Chaos in Chemical Kinetics (Oxford University Press, NY, 1995)

    Google Scholar 

  46. K. Showalter, Quadratic and cubic reaction–diffusion Fronts. Nonlinear Sci. Today 4(4), 1–10 (1995)

    MATH  Google Scholar 

  47. S. Strogatz, Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hyperion, New York, 2003)

    Google Scholar 

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

    Article  Google Scholar 

  49. M. Toiya, V.K. Vanag, I.R. Epstein, Diffusively coupled chemical oscillators in a microfluidic assembly. Angew. Chem. 120, 7867–7869 (2008)

    Article  Google Scholar 

  50. N. Tompkins, M.C. Cambria, A.L. Wang, M. Heymann, S. Fraden, Creation and perturbation of planar networks of chemical oscillators. Chaos 25, 064611 (2015)

    Article  Google Scholar 

  51. T. Tuma, A. Pantazi, M. Le Gallo, A. Sebastian, E. Eleftheriou, Stochastic phase-change neurons. Nature Nanotechnol. (2016). doi:10.1038/NNANO.2016.70

    Google Scholar 

  52. J.J. Tyson, Scaling and reducing the Field-Koros-Noyes mechanism of the BelousovZhabotinskii reaction. J. Phys. Chem. 86, 3006–3012 (1982)

    Article  Google Scholar 

  53. V.K. Vanag, I.R. Epstein, Pattern formation in a tunable medium: The Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001)

    Article  Google Scholar 

  54. K. Wiesenfeld, F. Moss, Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373, 33–36 (1995)

    Google Scholar 

  55. R.S. Williams, How we found the missing memristor. IEEE Spectr. 45, 28–35 (2008)

    Article  Google Scholar 

  56. A.T. Winfree, The Geometry of Biological Time (Springer, New York, 2001)

    Book  MATH  Google Scholar 

  57. A.M. Zhabotinsky, Periodical oxidation of malonic acid in solution (a study of the Belousov reaction kinetics). Biofizika 9, 306–311 (1964)

    Google Scholar 

Download references

Acknowledgements

We thank John Murray and Mark Spano for helpful discussions on neural models, and Richard Field and Sabrina Sobel for helpful conversations on BZ dynamics.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Harold M. Hastings .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Hastings, H.M., Hernandez, O.I., Jiang, L., Lai, B., Tensen, L., Yang, J. (2017). Dynamics of Biomimetic Electronic Artificial Neural Networks. In: In, V., Longhini, P., Palacios, A. (eds) Proceedings of the 4th International Conference on Applications in Nonlinear Dynamics (ICAND 2016). ICAND 2016. Lecture Notes in Networks and Systems, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-52621-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-52621-8_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52620-1

  • Online ISBN: 978-3-319-52621-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics