We show that a network of spiking neurons exhibits robust self-organizedcriticality if the synaptic efficacies follow realistic dynamics. Derivinganalytical expressions for the average coupling strengths and inter-spikeintervals, we demonstrate that networks with dynamical synapses exhibitcritical avalanche dynamics for a wide range of interaction parameters. Weprove that in the thermodynamical limit the network becomes critical for alllarge enough coupling parameters. We thereby explain experimental observationsin which cortical neurons show avalanche activity with the total intensity offiring events being distributed as a power-law.
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