Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
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....
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X03211037 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1110-757X 1687-0042 |