Analytical solution for dynamic of neuronal populations

Wentao Huang; Licheng Jiao; Shiping Ma; Yuelei Xu

Analytical solution for dynamic of neuronal populations

Wentao Huang, Licheng Jiao, Shiping Ma, Yuelei Xu

School of Medicine

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages	19-24
Number of pages	6
State	Published - Dec 1 2005
Event	15th International Conference on Artificial Neural Networks: Biological Inspirations - ICANN 2005 - Warsaw, Poland Duration: Sep 11 2005 → Sep 15 2005

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3696 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Conference on Artificial Neural Networks: Biological Inspirations - ICANN 2005
Country	Poland
City	Warsaw
Period	9/11/05 → 9/15/05

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

Fingerprint Dive into the research topics of 'Analytical solution for dynamic of neuronal populations'. Together they form a unique fingerprint.

Cite this

Huang, W., Jiao, L., Ma, S., & Xu, Y. (2005). Analytical solution for dynamic of neuronal populations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 19-24). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3696 LNCS).

Analytical solution for dynamic of neuronal populations. / Huang, Wentao; Jiao, Licheng; Ma, Shiping; Xu, Yuelei.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2005. p. 19-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3696 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Huang, W, Jiao, L, Ma, S & Xu, Y 2005, Analytical solution for dynamic of neuronal populations. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3696 LNCS, pp. 19-24, 15th International Conference on Artificial Neural Networks: Biological Inspirations - ICANN 2005, Warsaw, Poland, 9/11/05.

Huang W, Jiao L, Ma S, Xu Y. Analytical solution for dynamic of neuronal populations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2005. p. 19-24. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Huang, Wentao ; Jiao, Licheng ; Ma, Shiping ; Xu, Yuelei. / Analytical solution for dynamic of neuronal populations. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2005. pp. 19-24 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{b50cbfabeac944be91e8e700c2b67cd1,

title = "Analytical solution for dynamic of neuronal populations",

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.",

author = "Wentao Huang and Licheng Jiao and Shiping Ma and Yuelei Xu",

year = "2005",

month = dec,

day = "1",

language = "English (US)",

isbn = "3540287523",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "19--24",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

note = "15th International Conference on Artificial Neural Networks: Biological Inspirations - ICANN 2005 ; Conference date: 11-09-2005 Through 15-09-2005",

}

TY - GEN

T1 - Analytical solution for dynamic of neuronal populations

AU - Huang, Wentao

AU - Jiao, Licheng

AU - Ma, Shiping

AU - Xu, Yuelei

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33646170888&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646170888&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33646170888

SN - 3540287523

SN - 9783540287520

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 19

EP - 24

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 15th International Conference on Artificial Neural Networks: Biological Inspirations - ICANN 2005

Y2 - 11 September 2005 through 15 September 2005

ER -