A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions
arXiv:2002.08649 · doi:10.46298/mna.12583
Abstract
We investigate a stochastic network composed of Integrate-and-Fire spiking neurons, focusing on its mean-field asymptotics. We consider an invariant probability measure of the McKean-Vlasov equation and establish an explicit sufficient condition to ensure the local stability of this invariant distribution. Furthermore, we prove a conjecture proposed initially by J. Touboul and P. Robert regarding the bistable nature of a specific instance of this neuronal model.
References in corpus (5)
- Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
- A model for neural activity in the absence of external stimuli
- Long time behavior of a mean-field model of interacting neurons
- Fluctuation limits for mean-field interacting nonlinear Hawkes processes
- On a toy network of neurons interacting through their dendrites