Apparaît dans la collection : 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience
We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since the last discharge, i.e., the refractory period. In this extension we incorporate the elapsed since the penultimate discharge and we obtain a more complex system of integro-differential equations. For this new system we prove convergence to stationary state by means of Doeblin’s theory in the case of weak non-linearities in an appropriate functional setting, inspired by the case of the classical elapsed time equation. Moreover, we present some numerical simulations to observe how different firing rates can give different types of behaviors and to contrast them with theoretical results of both classical and extended models.
De Monica Colpi
De Albert Schwarz
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
