Coherence and incoherence in a globally coupled ensemble of pulse-emitting units

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Abstract
A general theory of coherent behavior (‘‘locking’’) in a globally coupled ensemble of pulse-emitting units is presented. Each unit is modeled as a dynamic threshold device with arbitrary excitability function and noise. The interaction is described by a general linear-response kernel that includes a transmission delay. In the bulk limit, the dynamics is solved exactly. Two types of solutions are studied, viz., coherent states with synchronous activity of all units and incoherent stationary states, and their stability is analyzed in the low-noise limit.