A mean-field model with discontinuous coefficients for interacting neurons
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it
Luogo: Aula seminari (piano terra) Dipartimento di Fisica
- Giovanni Alessandro Zanco (IST Wien)
We propose a new stochastic model for a system of interacting neurons that follow an integrate-and-fire dynamics with interaction that depends on the (random) spatial configuration of neurons and with discontinuous coefficients.
We prove strong well-posedness of the resulting system of SDEs and study the mean-field limit as the number of particles tends to infinity. We obtain a Fokker-Planck-type PDE and show that it has a unique weak function-valued solution, obtained as the limit of the laws of the empirical measures for the system of particles.
Referente: Stefano Bonaccorsi