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International Conference on Artificial Neural Networks

ICANN 2005: Artificial Neural Networks: Biological Inspirations – ICANN 2005 pp 19–24Cite as

Analytical Solution for Dynamic of Neuronal Populations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3696))

Abstract

The population density approach is a viable method to describe the large populations of neurons and has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation. Now, the discussion of most researchers is based on the population density function. In this paper, we propose a new function to characterize the population of excitatory and inhibitory spiking neurons and derive a novel evolution equation which is a nonhomogeneous parabolic type equation. Moreover, we study the stationary solution and give the firing rate of the stationary states. Then we solve for the time dependent solution using the Fourier transform, which can be used to analyze the various behavior of cerebra.

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References

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Author information

Authors and Affiliations

  1. Institute of Intelligent Information Processing and Key Laboratory, of Radar Signal Processing, Xidian University, Xi’an, 710071, China

    Wentao Huang & Licheng Jiao

  2. Signal and Information Processing Laboratory, Avionic Engineering Department, College of Engineering, Air Force Engineering University, Xi’an, 710038, China

    Wentao Huang, Shiping Ma & Yuelei Xu

Authors
  1. Wentao Huang
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  2. Licheng Jiao
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  3. Shiping Ma
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  4. Yuelei Xu
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Editor information

Editors and Affiliations

  1. Department of Informatics, Nicolaus Copernicus University, Toruń, Poland

    Włodzisław Duch

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

  3. Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland

    Erkki Oja

  4. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Sławomir Zadrożny

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© 2005 Springer-Verlag Berlin Heidelberg

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Cite this paper

Huang, W., Jiao, L., Ma, S., Xu, Y. (2005). Analytical Solution for Dynamic of Neuronal Populations. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Biological Inspirations – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550822_4

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  • DOI: https://doi.org/10.1007/11550822_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28752-0

  • Online ISBN: 978-3-540-28754-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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