@misc{10481/70824,
year = {2021},
month = {3},
url = {http://hdl.handle.net/10481/70824},
abstract = {The elapsed time model has been widely studied in the context of mathematical neuroscience with
many open questions left. The model consists of an age-structured equation that describes the dynamics
of interacting neurons structured by the elapsed time since their last discharge. Our interest lies in highly
connected networks leading to strong nonlinearities where perturbation methods do not apply. To deal
with this problem, we choose a particular case which can be reduced to delay equations.
We prove a general convergence result to a stationary state in the inhibitory and the weakly excitatory
cases. Moreover, we prove the existence of particular periodic solutions with jump discontinuities in the
strongly excitatory case. Finally, we present some numerical simulations which ilustrate various behaviors,
which are consistent with the theoretical results.},
organization = {European Commission	754362},
organization = {French National Research Agency (ANR)	ANR19CE400024},
publisher = {Elsevier},
keywords = {Structured equations},
keywords = {Mathematical neuroscience},
keywords = {Neural networks},
keywords = {Periodic solutions},
keywords = {Delay differential equations},
title = {An elapsed time model for strongly coupled inhibitory and excitatory neural networks},
author = {Cáceres Granados, María Josefa and Perthame, Benoît and Salort, Delphine and Torres, Nicolás},
}