Skip to main content

The Neuron’s Modeling Methods Based on Neurodynamics

  • Conference paper
  • 2588 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7367))

Abstract

In the paper, based on the neurodynamics theory, the neuron’s dynamic description and how to build the neuron’s dynamic model are analyzed and generalized from the dynamics angle. The building methods and the building procedures of the neuron model based on neurodynamics and electrophysiology are systematically put forward. The modeling methods and the modeling procedures are systematical summaries and sublimations of the neuron’s modeling theories and achievements in recent years, and have the important guiding significance for the neuron’s modeling based on the neurodynamics theory.

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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hodgkin, A.L., Huxley, A.F.: Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Journal of Physiology 116, 449–472 (1952)

    Google Scholar 

  2. Hodgkin, A.L., Huxley, A.F.: The components of membrane conductance in the giant axon of Loligo. Journal of Physiology 116, 473–496 (1952)

    Google Scholar 

  3. Hodgkin, A.L., Huxley, A.F.: The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. Journal of Physiology 116, 497–506 (1952)

    Google Scholar 

  4. Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane and its application to conduction and excitation in nerve. Journal of Physiology 117, 500–544 (1952)

    Google Scholar 

  5. Frankenhaeuser, B., Huxley, A.F.: The action potential in the myelinated nerve fivre of Xenpous laevis as computed on the basis of voltage clamp data. Journal of Physiology 171(4), 302–315 (1964)

    Google Scholar 

  6. Adrian, R.H., Chandler, W.K., Hodgkin, A.L.: Voltage clamp experiments in striated muscle fibres. Journal of Physiology 208(5), 607–644 (1970)

    Google Scholar 

  7. Adrian, R.H., Peachey, L.D.: Reconstruction of the action potential of frog sartorius muscle. Journal of Physiology 235(1), 103–131 (1973)

    Google Scholar 

  8. Noble, D.: A modification of the Hodgkin-Huxley equation applicable to Purkinje fibre action and pacemaker potentials. Journal of Physiology 160(3), 317–352 (1962)

    Google Scholar 

  9. McAllister, R.E., Noble, D., Tsien, R.W.: Reconstruction of the electrical activity of cardiac Purkinje fibers. Journal of Physiology 251(1), 1–58 (1975)

    Google Scholar 

  10. Beeler, G.W., Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres. Journal of Physiology 235(1), 103–131 (1977)

    Google Scholar 

  11. Morris, C., Lecar, H.: Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal 35(2), 193–213 (1981)

    Article  Google Scholar 

  12. Chay, T.R., Keizer, J.: Minimal model for membrane oscillations in the pancreatic beta-cell. Biophysical Journal 42(2), 181–190 (1983)

    Article  Google Scholar 

  13. Rinzel, J., Lee, Y.S.: Dissection of a model for neuronal parabolic bursting. Journal of Mathematical Biology 25(7), 653–675 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  14. Butera, R.J., Rinzel, J., Smith, J.C.: Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology 81(4), 382–397 (1999)

    Google Scholar 

  15. Dayan, P., Abbott, L.F. (eds.): Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. MIT Press, Cambridge (2002)

    Google Scholar 

  16. Brunel, N., Meunier, C., Fregnac, Y.: Neuroscience and computation. Journal of Physiology-Paris 97(4), 387–390 (2003)

    Article  Google Scholar 

  17. Ermentrout, G.: Type I membranes, phase resetting curves, and synchrony. Neural Computation 8(10), 979–1001 (1996)

    Article  Google Scholar 

  18. Ermentrout, G., Kopell, N.: Parabolic bursting in an excitable system coupled with a slow oscillation. SIAM Journal on Applied Mathematics 46(3), 223–253 (1986)

    Article  MathSciNet  Google Scholar 

  19. Hindmarsh, J.L., Rose, R.M.: A mode of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London, Series B, Biological Sciences 221(1222), 87–102 (1984)

    Article  Google Scholar 

  20. Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT Press (2005)

    Google Scholar 

  21. Hindmarsh, J.L., Rose, R.M.: A mode of the nerve impulse using two first-order differential equations. Nature 296, 162–164 (1982)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

He, X., Peng, Y., Gao, H. (2012). The Neuron’s Modeling Methods Based on Neurodynamics. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds) Advances in Neural Networks – ISNN 2012. ISNN 2012. Lecture Notes in Computer Science, vol 7367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31346-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31346-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31345-5

  • Online ISBN: 978-3-642-31346-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics