Publication 19-CNA-003

Self-similar spreading in a merging-splitting model of animal group size

Jian-Guo Liu
Departments of Physics and Mathematics
Duke University
Durham, NC 27708
jliu@phy.duke.edu

Barbara Niethammer
Institut für Angewandte Mathematik
Universität Bonn
53115 Bonn, Germany
niethammer@iam.uni-bonn.de

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@andrew.cmu.edu

Abstract: In a recent study of certain merging-splitting models of animal-group size (Degond et al., J. Nonl. Sci. 27 (2017) 379), it was shown that an initial size distribution with infinite first moment leads to convergence to zero in weak sense, corresponding to unbounded growth of group size. In the present paper we show that for any such initial distribution with a power-law tail, the solution approaches a self-similar spreading form. A one-parameter family of such self-similar solutions exists, with densities that are completely monotone, having power-law behavior in both small and large size regimes, with different exponents.

Get the paper in its entirety as  19-CNA-003.pdf

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