De Kota Ikeda
Apparaît dans la collection : 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience
In neural networks, fast global oscillations was observed in [1] and are named gamma oscillation. Among other models aimed at understanding the self-sustained oscillations, the NNLIF model with synaptic delay and weakly firing inhibitory neurons was developed two decades ago [2]. Periodic solutions have been numerically observed in this model, but despite intensive study of this model in several researches, there was up-to-date no analytical result on this topic. In this talk, we propose to approximate formally these solutions by a Gaussian wave whose periodic movement is described by an associate difference-differential equation. We prove the existence of a periodic solution for the position in time of the centre of the Gaussian wave and we give a rigorous asymptotic result on these solutions when the connectivity parameter $b$ goes to $−∞$. Finally we provide heuristic and numerical evidence of the validity of our approximation.
De Monica Colpi
De Albert Schwarz
De Albert Schwarz
De Juan Camilo Arosemena Serrato
De Francesca Arici
De Amine Marrakchi
