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Some PDE models for neural networks. The blow-up phenomenon for NNLIF models

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FKTW03 - Frontiers in kinetic equations for plasmas and collective behaviour

In recent decades, a kinetic theory description has been developed to model the collective behavior of large ensembles of neurons in a neural network. A macroscopic representation of the dynamics of the network was derived directly from the microscopic dynamics of individual neurons. Therefore, different approaches led to different PDE models for the probability density function of neuronal membrane potentials and synaptic conductances. In this talk we analyze some of these models. And we show the wide variety of properties that the solutions of these models present and that are in agreement with the observed phenomena of neural networks: bistability, synchronous and asynchronous solutions, blow-up phenomena,...

This talk is part of the Isaac Newton Institute Seminar Series series.

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