Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Towards a further understanding of the dynamics in NNLIF models: blow-up, global existence and coupled networks

Abstract : The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a stochastic differential equation. In previous works, many qualitative results were obtained: global existence in the inhibitory case, finite time blow-up in the excitatory case, convergence towards stationary states in the weak connectivity regime. In this article, we refine some of these results in order to foster the understanding of the model. We prove with deterministic tools that blow-up is systematic in highly connected excitatory networks. Then we study the impact of excitatory-inhibitory coupling on finite time blow-up. Finally, we show that a relatively weak control on the firing rate suffices to obtain global-in-time strong solutions.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02508412
Contributor : Pierre Roux <>
Submitted on : Saturday, March 14, 2020 - 4:10:39 PM
Last modification on : Monday, August 31, 2020 - 12:30:22 PM
Long-term archiving on: : Monday, June 15, 2020 - 1:13:11 PM

File

ArticleNNLIF.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02508412, version 1

Citation

Pierre Roux, Delphine Salort. Towards a further understanding of the dynamics in NNLIF models: blow-up, global existence and coupled networks. 2020. ⟨hal-02508412⟩

Share

Metrics

Record views

76

Files downloads

84