Journal Article

Dynamics of group formation in collective motion of organisms

Petro Babak, Kjartan G. Magnússon and Sven Sigurdsson

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 4, pages 269-292
Published in print December 2004 | ISSN: 1477-8599
Published online December 2004 | e-ISSN: 1477-8602 | DOI:
Dynamics of group formation in collective motion of organisms

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  • Applied Mathematics
  • Biomathematics and Statistics


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A mathematical description of the collective motion of organisms using a density–velocity model is presented. This model consists of a system of nonlinear parabolic equations, a forced Burgers equation for velocity and a diffusion–convection equation for density. The motion is mainly due to forces resulting from the differences between local density levels and a prescribed density level.

The existence of a global attractor for a 1D density–velocity model is proved by asymptotic analysis to demonstrate different patterns in the attractors for density. The theoretical results are supplemented with numerical results. These patterns correspond to movements of collective organized groups of organisms such as fish schools and bird flocks.

Keywords: attractors; Burgers equation; diffusion–convection equation; collective organization

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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