Abstract:
We present a simple model that displays all classes of two-dimensional excitable regimes. One of the variables of the model displays the usual spikes observed in excitable systems. Since the model is written in terms of a “standard” vector field, it is always possible to fit it to experimental data displaying spikes in an algorithmic way. In fact, we use it to fit a series of membrane potential recordings obtained in the medicinal leech and time series generated with the FitzHugh-Nagumo equations and the excitability model of Eguía et al. [Phys. Rev. E 58, 2636 (1998)]. In each case, we determine the excitability class of the corresponding system. © 2002 The American Physical Society.
Registro:
| Documento: |
Artículo
|
| Título: | Generic two-variable model of excitability |
| Autor: | Ventura, A.C.; Mindlin, G.B.; Dawson, S.P. |
| Filiación: | Departamento de Física, FCEN, UBA Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina
|
| Año: | 2002
|
| Volumen: | 65
|
| Número: | 4
|
| Página de inicio: | 7
|
| DOI: |
http://dx.doi.org/10.1103/PhysRevE.65.046231 |
| Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|
| Título revista abreviado: | Phys Rev E.
|
| ISSN: | 1063651X
|
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v65_n4_p7_Ventura |
Referencias:
- Coullet, P.C., Müller, S.C., Walgraef, D., (1994) Chaos, 4, p. 439
- F.C. Hoppensteadt and E.M. Izhikevich, Weakly Connected Neural Networks (Springer, New York, 1997); Yacomotti, A.M., Eguía, M.C., Aliaga, J., Martínez, O.E., Mindlin, G.B., Lipsich, A., (1999) Phys. Rev. Lett., 83, p. 292
- J.D. Murray, Mathematical Biology (Springer, New York, 1989); Hodgkin, A.L., Huxley, A.F., (1952) J. Physiol. (London), 117, p. 500
- Eguía, M.C., Mindlin, G.B., Giudici, M., (1998) Phys. Rev. E, 58, p. 2636
- J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, New York, 1986), p. 365; M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory (Springer, New York, 1985), Vol. I, p. 121; D.K. Arrowsmith and C.M. Place, An Introduction to Dynamical Systems (Cambridge University Press, Cambridge, 1990), p. 76; Gouesbet, G., (1991) Phys. Rev. A, 43, p. 5321
- The data was provided by L. Szczupak (Department of Biology, FCEN, UBA). The membrane potential was recorded every 2 ms. Since the large excursion part of the action potentials last 10 ms, the data were interpolated with a cubic spline; Ohta, T., Hayase, Y., Kobayashi, R., (1996) Phys. Rev. E, 54, p. 6074
- Lee, K.J., McCormick, W.D., Pearson, J.E., Swinney, H.L., (1994) Nature (London), 369, p. 215
- Ponce Dawson, S., D’Angelo, M.V., Pearson, J.E., (2000) Phys. Lett. A, 265, p. 346
- M.V. D’Angelo and S. Ponce Dawson (unpublished); Gray, P., Scott, S., (1983) Chem. Eng. Sci., 38, p. 29
- Pearson, J.E., (1993) Science, 261, p. 189
Citas:
---------- APA ----------
Ventura, A.C., Mindlin, G.B. & Dawson, S.P.
(2002)
. Generic two-variable model of excitability. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 65(4), 7.
http://dx.doi.org/10.1103/PhysRevE.65.046231---------- CHICAGO ----------
Ventura, A.C., Mindlin, G.B., Dawson, S.P.
"Generic two-variable model of excitability"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 65, no. 4
(2002) : 7.
http://dx.doi.org/10.1103/PhysRevE.65.046231---------- MLA ----------
Ventura, A.C., Mindlin, G.B., Dawson, S.P.
"Generic two-variable model of excitability"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 65, no. 4, 2002, pp. 7.
http://dx.doi.org/10.1103/PhysRevE.65.046231---------- VANCOUVER ----------
Ventura, A.C., Mindlin, G.B., Dawson, S.P. Generic two-variable model of excitability. Phys Rev E. 2002;65(4):7.
http://dx.doi.org/10.1103/PhysRevE.65.046231
