Relaxation and self-sustained oscillations in the time elapsed neuron network model
The time elapsed model for neural networks has been introduced and studied by the authors in a previous paper [Nonlinearity 23, No. 1, 55--75 (2010; Zbl 1267.35239)]. The aim here is a further discussion on the convergence to asynchronous states and the construction of explicit periodic solutions in case assembly does not converge to the asynchronous state. After a presentation of the time elapsed model, results on convergence are proved in the sections `Dynamics of ensembles of disconnected neurons' and `Asynchronous activity for connected neuronal assemblies'. The section `Synchronous periodic oscillations in neuronal assemblies' is devoted to the construction of periodic solutions. Simulation results are shown.
scientific article; zbMATH DE number 6212915