In a coupled network of excitable elements that are initially at rest, the application of a transient, spatially localized stimulus can lead to the propagation of activity throughout the network, a small burst of activity that dies out, or an intermediate state of sustained, localized activity. For propagation to result, silent elements must be recruited to become active. This recruitment can fail through the build-up of inhibitory coupling, but even without inhibition, it can fail through the desynchronization of active cells. We give a geometric analysis of the degree of desynchronization for which recruitment fails in networks composed of certain types of elements, corresponding to some particular neuronal models.
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