A multiple time renewal equation for neural assemblies with elapsed time model.

Abstract: 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 last discharge. 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.

Date: Aug 23, 2022 at 12:00:00 h
Venue: Sala de Seminario John Von Neuman, CMM, Beauchef 851, Torre Norte, Piso 7.
Speaker: Nicolas Torres
Affiliation: Université Claude Bernard Lyon 1, Francia
Coordinator: Gabrielle Nornberg
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Posted on Aug 19, 2022 in Differential Equations, Seminars