Global-in-time solutions and qualitative properties for the NNLIF neuron model with synaptic delay

DOI10.1080/03605302.2019.1639732zbMath1423.35148arXiv1806.01934OpenAlexW2963032419WikidataQ127472910 ScholiaQ127472910MaRDI QIDQ5239044

Maria José Cáceres, Ricarda Schneider, Delphine Salort, Pierre Roux

Publication date: 21 October 2019

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.01934

zbMATH Keywords

noisedelayneural networksblow-upStefan problemglobal existenceleaky integrate and fire modelsrelaxation to steady state

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Neural networks for/in biological studies, artificial life and related topics (92B20) Initial-boundary value problems for second-order parabolic equations (35K20) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Free boundary problems for PDEs (35R35) Blow-up in context of PDEs (35B44) Fokker-Planck equations (35Q84)

Related Items (7)

Rigorous Justification of the Fokker--Planck Equations of Neural Networks Based on an Iteration Perspective ⋮ A Structure Preserving Numerical Scheme for Fokker--Planck Equations of Structured Neural Networks with Learning Rules ⋮ Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results ⋮ Concentration profiles in FitzHugh-Nagumo neural networks: a Hopf-Cole approach ⋮ An Understanding of the Physical Solutions and the Blow-Up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models ⋮ Long time behavior of a mean-field model of interacting neurons ⋮ Towards a further understanding of the dynamics in the excitatory NNLIF neuron model: blow-up and global existence

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