Effects of spatial connectivity and delays on spatio-temporal dynamics of cortical networks models

Nicolas Brunel
CNRS, Paris 5
France

Abstract

One of the major goals of theoretical neuroscience is to understand the relationship between the spatial and functional organization of cortical circuits and the intrinsic spatio-temporal dynamics of neuronal activity. We investigated the spatio-temporal dynamics of large networks of neurons with delayed synaptic communication and spatially organized connectivity, and found a rich diversity of spatio-temporal states: oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period doubling bifurcation and aperiodic regimes. These states can be observed in both networks of spiking neurons and firing rate models, in which the existence and the stability of the various dynamical patterns can be studied analytically and numerically as a function of the parameters describing the spatial structure of the network. In both types of models, we identified several regions of bistability between spatially uniform oscillatory states and spatially modulated oscillatory states in purely inhibitory networks with spatially decaying connectivity. This bistability could endow such a purely inhibitory network with short-term memory properties.

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