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29 June 2003 Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
Nikola V. Georgiev
J. Appl. Math. 2003(8): 397-407 (29 June 2003). DOI: 10.1155/S1110757X03211037


An analytic time series in the form of numerical solution (in an appropriate finite time interval) of the Hodgkin-Huxley current clamped (HHCC) system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN) type, having as a solution the given single component (action potential) of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation) and a specific modification of least squares method for identifying unknown coefficients are developed and applied.


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Nikola V. Georgiev. "Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model." J. Appl. Math. 2003 (8) 397 - 407, 29 June 2003.


Published: 29 June 2003
First available in Project Euclid: 3 July 2003

zbMATH: 1077.37524
MathSciNet: MR1996326
Digital Object Identifier: 10.1155/S1110757X03211037

Primary: 37N30 , 93C15

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 8 • 29 June 2003
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