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Research Papers

Parameter Estimation of the FitzHugh–Nagumo Neuron Model Using Integrals Over Finite Time Periods

[+] Author and Article Information
Antonio Concha

Instituto de Ingeniería,
Universidad Nacional Autónoma de México,
Coyoacán, D.F 04510, Mexico
e-mail: AConchaS@iingen.unam.mx

Rubén Garrido

Professor
Departamento de Control Automático,
Centro de Investigación y de Estudios Avanzados
del Instituto Politécnico Nacional,
Gustavo A. Madero, D.F 07360, Mexico
e-mail: garrido@ctrl.cinvestav.mx

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 8, 2014; final manuscript received September 12, 2014; published online January 21, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 10(2), 021023 (Mar 01, 2015) (6 pages) Paper No: CND-14-1094; doi: 10.1115/1.4028601 History: Received April 08, 2014; Revised September 12, 2014; Online January 21, 2015

This paper proposes two methodologies for estimating the parameters of the FitzHugh–Nagumo (FHN) neuron model. The identification procedures use only measurements of the membrane potential. The first technique is named the identification method based on integrals and wavelets (IMIW), which combines a parameterization based on integrals over finite time periods and a wavelet denoising technique for removing the measurement noise. The second technique, termed as the identification method based only on integrals (IMOI), does not use any wavelet denoising technique and attenuates the measurement noise by integrating the IMIW parameterization two times more over finite time periods. Both procedures use the least squares algorithm for estimating the FHN parameters. Integrating the FHN model over finite time periods allows eliminating the unmeasurable recovery variable of this model, thus obtaining a parameterization based on integrals of the measurable membrane potential variable. Unlike an identification technique recently published, the proposed methods do not rely on the time derivatives of the membrane potential and are not limited to continuously differentiable input current stimulus. Numerical simulations show that both the IMIW and IMOI have a good and a similar performance, however, the implementation of the latter is simpler than the implementation of the former.

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Figures

Grahic Jump Location
Fig. 1

Bode diagram gain of the filters Gi(s), i = 0, 1, 2. (a) G0(s), (b) G1(s), and (c) G2(s).

Grahic Jump Location
Fig. 2

Spectrum of x1m. (a) Spectrum of x1m when u = u1, (b) Spectrum of x1m when u = u2.

Grahic Jump Location
Fig. 3

Signals x1, x1m, and x1w. (a) x1m and (b). x1 versus x1w.

Grahic Jump Location
Fig. 4

Comparison of the predicted and nominal signals. (a) x1 versus x∧1 and (b) x2 versus x∧2.

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