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- W2805094736 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 system. When the total activity of the network has an instantaneous effect on the network, in the average-excitatory case, a blow-up phenomenon occurs. This article is devoted to the theoretical study of the NNLIF model in the case where a delay in the effect of the total activity on the neurons is added. We first prove global-in-time existence and uniqueness of classical solutions, independently of the sign of the connectivity parameter, that is, for both cases: excitatory and inhibitory. Secondly, we prove some qualitative properties of solutions: asymptotic convergence to the stationary state for weak interconnections and a non-existence result for periodic solutions if the connectivity parameter is large enough. The proofs are mainly based on an appropriate change of variables to rewrite the NNLIF equation as a Stefan-like free boundary problem, constructions of universal super-solutions, the entropy dissipation method and Poincare's inequality." @default.
- W2805094736 created "2018-06-13" @default.
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- W2805094736 date "2018-06-04" @default.
- W2805094736 modified "2023-09-25" @default.
- W2805094736 title "Global-in-time classical solutions and qualitative properties for the NNLIF neuron model with synaptic delay" @default.
- W2805094736 hasPublicationYear "2018" @default.
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