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On the Integrate-and-Fire model with superlinear drift
Benoît Perthame, Clément Rieutord, Delphine Salort
The Nonlinear Integrate-and-Fire equation is a fundamental model for neural assemblies, describing the dynamics of the density of neurons with a given potential. Its standard formu…
Asymptotic dynamics of inhibitory networks for the NNLIF Model in the large-delay limit
Clément Rieutord, Delphine Salort
We investigate the impact of large synaptic delays on the emergence of periodic dynamics in inhibitory neuronal networks, within the framework of the NNLIF model. Inspired by the w…
A Fokker-Planck equation with superlinear drift at infinity for Integrate-and-Fire model
Benoît Perthame, Clément Rieutord, Delphine Salort
The Integrate-and-Fire model is a Fokker-Planck equation arising in neuroscience. It describes the evolution of the probability density of the neuronal membrane potential and fitti…
Strongly nonlinear age structured equation,time-elapsed model and large delays
Benoît Perthame, Delphine Salort, Clément Rieutord
The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly wi…