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An Isaac Newton Institute Workshop

Theory and Applications of Coupled Cell Networks

Rate models with delays and the dynamics of large networks of spiking neurons

Author: D. Hansel (Neurophysique et Physiologie du Systeme Moteur, CNRS- Universite Rene Descartes, 45 Rue des Saints Peres, 75270, Paris, France)

Abstract

We investigate the dynamics of a one-dimensional network of spiking neurons with spatially modulated excitatory and inhibitory interactions through extensive numerical simulations. We find that the network displays a very rich phase diagram as a function of the interaction parameters. Dynamical states include homogeneous oscillations, oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period doubling bifurcation, aperiodic regimes and regimes of multistability. We show that a similar diversity is found in the framework of a reduced rate model in which the interactions are delayed. A great deal of this study can be performed analytically. Our work suggests that the delay in the response of the neurons to their synaptic inputs due to the non-linearity underlying spike generation have important consequences for the collective dynamics of large neuronal systems.