Event Details

Título: An understanding of the physical solutions and the blow-up phenomenon for Nonlinear Noisy Leaky Integrate and Fire neuronal models.
Impartida por: Alejandro Ramos Lora.
Fecha: 10 de marzo de 2021 de 12:00-13:00.
Resumen: The Nonlinear Noisy Leaky Integrate and Fire neuronal models are mathematical models that describe the activity of neural networks. These models have been studied at a microscopic level, using Stochastic Differential Equations, and at a mesoscopic/macroscopic level, through the mean field limits using Fokker-Planck type equations. To analyse in depth the behaviour of the classical and physical solutions of the Stochastic Differential Equations and, comparing it with what is already known about the Fokker-Planck equation, allows us to better understand what happens in the neural network when an explosion occurs in finite time. After firing all neurons at the same time, if the system is weakly connected, the neural network converges towards its unique steady state. Otherwise, its behaviour is more complex, because it can tend towards a stationary state or a "plateau" distribution.
Link de la reunión: https://meet.google.com/yrc-wpte-dbj