Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model

DOI10.1007/s00285-016-1002-8zbMath1358.35202arXiv1512.03785OpenAlexW2285573522WikidataQ47713263 ScholiaQ47713263MaRDI QIDQ338335

Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu

Publication date: 4 November 2016

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03785

zbMATH Keywords

neural networksage-structured modelFokker-Plank modelFPNLIFnoisy leaky integrate-and-fire models

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fokker-Planck equations (35Q84)

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Cites Work

• Unnamed Item
• Unnamed Item
• Theoretical connections between mathematical neuronal models corresponding to different expressions of noise
• Population density models of integrate-and-fire neurons with jumps: well-posedness
• Synchronization of an excitatory integrate-and-fire neural network
• Lapicque's 1907 paper: from frogs to integrate-and-fire
• Dynamics of current-based, Poisson driven, integrate-and-fire neuronal networks
• Mathematical foundations of neuroscience
• A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application in orientation tuning
• On the simulation of large populations of neurons.
• Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.
• Analysis of nonlinear noisy integrate \& fire neuron models: blow-up and steady states
• A density model for a population of theta neurons
• A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input
• Relaxation and Self-Sustained Oscillations in the Time Elapsed Neuron Network Model
• Spiking Neuron Models
• Classical Solutions for a Nonlinear Fokker-Planck Equation Arising in Computational Neuroscience
• The Narrow Escape Problem
• Dynamics of a structured neuron population
• Handbook of stochastic methods for physics, chemistry and natural sciences.

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