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

Nikola V. Georgiev

Journal of Applied Mathematics, 2003, vol. 2003, issue 8, 397-407

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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https://doi.org/10.1155/S1110757X03211037

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2003:y:2003:i:8:p:397-407

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