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Collective Behavior of Feedback Networks with Distributed Dynamics

We analyze the collective behavior of feedback neural networks with discrete-time dynamics in which groups of one or more neurons may change their state simultaneously. Such partially parallel updating rules generalize beyond the one-at-a-time dynamics of the Hopfield model and the fully synchronous dynamics of the Little model. We derive sufficient conditions under which this type of distributed network dynamics leads to fixed point attractors only and report quantitative results on the emergent network properties.