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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 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03324280
Contributor : Nicolas Torres Connect in order to contact the contributor
Submitted on : Tuesday, September 14, 2021 - 10:41:37 PM
Last modification on : Tuesday, September 28, 2021 - 5:16:45 PM

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  • HAL Id : hal-03324280, version 2
  • ARXIV : 2108.10577

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Nicolás Torres, Benoît Perthame, Delphine Salort. A multiple time renewal equation for neural assemblies with elapsed time model. 2021. ⟨hal-03324280v2⟩

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