Self-similar Spreading in a Merging-Splitting Model of Animal Group Size

Published

Journal Article

© 2019, Springer Science+Business Media, LLC, part of Springer Nature. In a recent study of certain merging-splitting models of animal-group size (Degond et al. in J Nonlinear Sci 27(2):379–424, 2017), 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.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Niethammer, B; Pego, RL

Published Date

  • June 30, 2019

Published In

Volume / Issue

  • 175 / 6

Start / End Page

  • 1311 - 1330

International Standard Serial Number (ISSN)

  • 0022-4715

Digital Object Identifier (DOI)

  • 10.1007/s10955-019-02280-w

Citation Source

  • Scopus