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

Nikola V. Georgiev

Journal of Applied Mathematics, 2003, vol. 2003, 1-11

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:726768

DOI: 10.1155/S1110757X03211037

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