PMID: 9540051Apr 16, 1998Paper

Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks

Journal of Computational Neuroscience
Henry C Tuckwell, R Rodriguez

Abstract

An analytical approach is presented for determining the response of a neuron or of the activity in a network of connected neurons, represented by systems of nonlinear ordinary stochastic differential equations--the Fitzhugh-Nagumo system with Gaussian white noise current. For a single neuron, five equations hold for the first- and second-order central moments of the voltage and recovery variables. From this system we obtain, under certain assumptions, five differential equations for the means, variances, and covariance of the two components. One may use these quantities to estimate the probability that a neuron is emitting an action potential at any given time. The differential equations are solved by numerical methods. We also perform simulations on the stochastic Fitzugh-Nagumo system and compare the results with those obtained from the differential equations for both sustained and intermittent deterministic current inputs with superimposed noise. For intermittent currents, which mimic synaptic input, the agreement between the analytical and simulation results for the moments is excellent. For sustained input, the analytical approximations perform well for small noise as there is excellent agreement for the moments. In additi...Continue Reading

Citations

Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J A AcebrónW-J Rappel
Mar 6, 2008·Nature Reviews. Neuroscience·A Aldo FaisalDaniel M Wolpert
Jan 22, 2010·PLoS Computational Biology·Nicolas TabareauQuang-Cuong Pham
Feb 20, 2003·Neural Computation·Henry C TuckwellFrederic Y M Wan
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gustavo Deco, Daniel Martí
Jun 21, 2011·Nature Reviews. Neuroscience·Mark D McDonnell, Lawrence M Ward
May 9, 2008·PLoS Computational Biology·Antti SaarinenOlli Yli-Harja
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Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Sep 28, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Sep 28, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideo Hasegawa
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Pablo KaluzaHildegard Meyer-Ortmanns
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Apr 18, 2021·Physical Review. E·Emre BaspinarAnna Zakharova
Feb 17, 2000·Trends in Neurosciences·J A WhiteA R Kay

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