Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches.

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