Stochastic Integrate and Fire Models: a review on mathematical methods\n and their applications

2011/01/28 by Laura Sacerdote, Sacerdote, Laura, Marı́a Teresa Giraudo +1 · 1 citation
Neuroscience · Physics and Astronomy · #60G07 #92B05 #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Probability (math.PR) #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1101.5539

openalex publication_date 2011/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mathematical models are an important tool for neuroscientists. During the\nlast thirty years many papers have appeared on single neuron description and\nspecifically on stochastic Integrate and Fire models. Analytical results have\nbeen proved and numerical and simulation methods have been developed for their\nstudy. Reviews appeared recently collect the main features of these models but\ndo not focus on the methodologies employed to obtain them. Aim of this paper is\nto fill this gap by upgrading old reviews on this topic. The idea is to collect\nthe existing methods and the available analytical results for the most common\none dimensional stochastic Integrate and Fire models to make them available for\nstudies on networks. An effort to unify the mathematical notations is also\nmade. This review is divided in two parts: Derivation of the models with the\nlist of the available closed forms expressions for their characterization;\nPresentation of the existing mathematical and statistical methods for the study\nof these models.\n

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