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math.PR2020★ 19 cited
Hopf bifurcation in a Mean-Field model of spiking neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study a family of non-linear McKean-Vlasov SDEs driven by a Poisson measure, modelling the mean-field asymptotic of a network of generalized Integrate-and-Fire neurons. We give…
math.PR2018★ 28 cited
Long time behavior of a mean-field model of interacting neurons
Quentin Cormier, Etienne Tanré, Romain Veltz
We study the long time behavior of the solution to some McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymp…