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

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

  • *Email: cai@cims.nyu.edu
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Phys. Rev. E 80, 021904 – Published 6 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021904

Abstract

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.

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Phys. Rev. E 80, 021904– Published 6 August, 2009
  • Received 3 April 2009

© 2009 American Physical Society

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