BECAS
MARTINEZ Nataniel
artículos
Título:
ON THE DURATION OF A SPIKE IN EXCITABLE DYNAMICAL SYSTEMS
Autor/es:
DEZA, IGNACIO; MARTÍNEZ, NATANIEL; DEZA, ROBERTO R.
Revista:
Matemática Aplicada, Computacional e Industrial
Editorial:
Asociación Argentina de Matemática Aplicada, Computacional e Industrial
Referencias:
Lugar: Santa Fe; Año: 2019 vol. 7 p. 561 - 564
ISSN:
2314-3282
Resumen:
Action potentialsor spikesare the carriers of information in neural tissue, and provide the mechanism for the synchronous motion of cardiac tissue. From a dynamical systems viewpoint, one speaks of an excitable regime. The notion of nonequilibrium potential (NEP) provides a global Lyapunov function (and thus, an energy landscape) to dissipative dynamical systems. Excitable behavior can then be explained in part by this landscape, and largely by the dynamical role of nonzero probability currents. The latter act as conservative forces, in the sense that they are normal to the gradient of the NEP. We show here that the argument whereby the NEP is shown to be a Lyapunov function, allows to determine the duration of a spike. This point is illustrated with the WilsonCowan model, a mean-field reduction of a neural network for which a NEP has been recently found