Population density models of integrate-and-fire neurons with jumps: well-posedness

DOI10.1007/S00285-012-0554-5zbMath1273.35012OpenAlexW2047931881WikidataQ47776020 ScholiaQ47776020MaRDI QIDQ365686

Grégory Dumont, Jacques Henry

Publication date: 9 September 2013

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

Full work available at URL: https://hal.inria.fr/hal-00711492/file/article-revised-V5.pdf

zbMATH Keywords

well-posednesscoupled populationexcitatory and inhibitory population modelspopulation density approach

Mathematics Subject Classification ID

Neural nets applied to problems in time-dependent statistical mechanics (82C32) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Integro-partial differential equations (35R09) Biological rhythms and synchronization (92B25) Initial-boundary value problems for nonlinear first-order PDEs (35F31)

Related Items (12)

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise ⋮ Beyond blow-up in excitatory integrate and fire neuronal networks: refractory period and spontaneous activity ⋮ A new firing paradigm for integrate and fire stochastic neuronal models ⋮ Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model ⋮ Synchronization of an excitatory integrate-and-fire neural network ⋮ Joint statistics of strongly correlated neurons via dimensionality reduction ⋮ The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states ⋮ Analysis and numerical solver for excitatory-inhibitory networks with delay and refractory periods ⋮ An Understanding of the Physical Solutions and the Blow-Up Phenomenon for Nonlinear Noisy Leaky Integrate and Fire Neuronal Models ⋮ A density model for a population of theta neurons ⋮ High order WENO finite volume approximation for population density neuron model ⋮ Global-in-time solutions and qualitative properties for the NNLIF neuron model with synaptic delay

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