On the duration of a spike in excitable dynamical systems

J. I. DEZA; N. MARTINEZ; R. R. DEZA

Rio Cuarto Córdoba

Congreso; VII Congreso de Matemática Aplicada, Computacional e Industrial - MACI 2019.; 2019

Asociación Argentina de Matemática Aplicada, Computacional e Industrial

Action potentials?or ?spikes??are 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 Wilson?Cowan model, a mean-field reduction of a neural network for which a NEP has been recently found.