Abstract
We study a locally nonconservative self-organized branching process (SOBP) in an open system of excitable agents exhibiting spontaneous excitation and deexcitation. The SOBP achieves criticality even in the absence of energy conservation as the population relaxes to a stable state with no overexcited agent. Criticality is widely thought to happen only in a locally conservative SOBP. Our model explains the observed characteristic size in the size distribution of tuna fish schools and the neuronal avalanches in cortical networks.
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