Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 726768 | https://doi.org/10.1155/S1110757X03211037

Nikola V. Georgiev, "Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model", Journal of Applied Mathematics, vol. 2003, Article ID 726768, 11 pages, 2003. https://doi.org/10.1155/S1110757X03211037

Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

Received25 Nov 2002
Revised16 Jan 2003

Abstract

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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