E8 Network dynamics (firing rate models)

Title

At the scale of neuronal populations, it is useful to describe activity not in terms of individual firings but of average firing rates of excitatory and inhibitory populations. The Wilson-Cowan model describes the temporal evolution of the rate of a population as a relaxation towards a value determined by a sigmoid gain function applied to the net input received (recurrent intra- and inter-population connections plus external input). Generalizing to n populations or units coupled through a connectivity matrix W, the complete system can be analyzed by its fixed points and by the linear stability of these through the Jacobian of the system, which allows predicting transitions between regimes of low activity, sustained activity or oscillations (linking with E09). A continuous mean field extension replaces the discrete matrix with a spatial connectivity core, useful for modeling cortical maps.

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