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Coagulation-fragmentation model for animal group-size statistics (15-CNA-017)

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journal contribution
posted on 20.10.2015, 00:00 by Pierre Degond, Jian-Guo Liu, Robert PegoRobert Pego

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent −2/3 for small size to −3/2 for large size, with an exponential cut-off.