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Updated: May 21, 2026
Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
Published on: March 2, 2015
Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states
María J Cáceres1, José A Carrillo, Benoît Perthame
1Departamento de Matemática Aplicada, Universidad de Granada, E-18071, Granada, Spain. caceresg@ugr.es.
Abstract:
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.AMS Subject Classification: 35K60, 82C31, 92B20.
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