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arXiv · 1510.06077

Coagulation-fragmentation model for animal group-size statistics

Pierre Degond·Jian-Guo Liu·Robert L. Pego
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Abstract

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 $-\frac23$ for small size to $-\frac32$ for large size, with an exponential cut-off.

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Pierre Degond, Jian-Guo Liu, Robert L. Pego. 2015-10-20. Coagulation-fragmentation model for animal group-size statistics. https://doi.org/10.1007/s00332-016-9336-3

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