This was part of Laplacian Growth Models

Spontaneous oscillations in purely excitatory network of IF type neurons

Etienne Tanré, Institut National de Recherche en Informatique et Automatique (INRIA)

Thursday, June 29, 2023

We consider a system of neurons of Integrate and Fire types. Each time their membrane potential spikes, the connected post-synaptic neurons receive a small `kick’.  The asymptotic behavior of a typical neuron is related to the Stefan problem.  It solves a McKean-Vlasov Stochastic Differential Integration with interaction through the law of the spiking times. The study of the limit equation highlights spontaneous oscillation behavior, even in the case of purely excitatory interactions.