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APS » Journals » Phys. Rev. E » Volume 80 » Issue 2
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Phys. Rev. E 80, 021904 (2009) [15 pages]

Fokker-Planck description of conductance-based integrate-and-fire neuronal networks

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Gregor Kovačič1, Louis Tao2, Aaditya V. Rangan3, and David Cai3,4,*
1Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA
2Center for Bioinformatics, National Laboratory of Protein Engineering and Plant Genetics Engineering, College of Life Sciences, Peking University, 5 Summer Palace Road, Beijing 100871, People’s Republic of China
3Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1185, USA
4Department of Mathematics, Shanghai Jiao Tong University, Dong Chuan Road 800, Shanghai 200240, People’s Republic of China

Received 3 April 2009; revised 27 June 2009; published 6 August 2009

Steady dynamics of coupled conductance-based integrate-and-fire neuronal networks in the limit of small fluctuations is studied via the equilibrium states of a Fokker-Planck equation. An asymptotic approximation for the membrane-potential probability density function is derived and the corresponding gain curves are found. Validity conditions are discussed for the Fokker-Planck description and verified via direct numerical simulations.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.80.021904
DOI:
10.1103/PhysRevE.80.021904
PACS:
87.19.L−, 05.20.Dd, 84.35.+i

*Email: cai@cims.nyu.edu

 
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