Stochastic Processes and Hitting Times in Mathematical Neurosciences - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Other Publications Year : 2006

Stochastic Processes and Hitting Times in Mathematical Neurosciences

Abstract

In this research report we define a new event-based mathematical framework for studying the dynamics of networks of integrate-and-fire neuron driven by external noise. Such networks are classically studied using the Fokker-Planck equation (Brunel, Hakim). In this study, we use the powerful tools developed for communication networks theory and define a formalism for the study of spiking neuron networks driven by an external noise. With this formalism, we address biological questions to characterize the different network regimes. In this framework, the probability distribution of the interspike interval is a fundamental parameter. We developed and apply several tools for defining and computing the probability density function (pdf) of the time of the first spike, using stochastic analysis. This point of view gives us an event-driven strategy for simulating this type of random networks. This strategy has been implemented in an extension of the event-driven simulator Mvaspike.
Fichier principal
Vignette du fichier
masterThesis.pdf (1.3 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00311967 , version 1 (22-08-2008)

Identifiers

  • HAL Id : inria-00311967 , version 1

Cite

Jonathan Touboul. Stochastic Processes and Hitting Times in Mathematical Neurosciences. 2006. ⟨inria-00311967⟩
108 View
58 Download

Share

Gmail Facebook Twitter LinkedIn More