Open Access
June 2008 A simple model for biological aggregation with asymmetric sensing
P. A. Milewski, X. Yang
Commun. Math. Sci. 6(2): 397-416 (June 2008).


In this paper we introduce a simple continuum model for swarming of organisms in which there is a nonlocal aggregation term with an asymmetric sensing kernel countered by a nonlinear diffusion. The model can be thought of as capturing the dynamics of organisms that aggregate responding to visual cues and whose field of vision is predominantly in the direction of motion. The model has a variety of traveling solutions, including compact swarms where the speed of the swarm increases with the total number of organisms in the swarm (up to a largest swarm), traveling fronts and periodic waves. The dynamics of fully time-dependent solutions include complicated inelastic swarm interactions and the spontaneous breakup of small populations into compact swarms. We also comment on a kinetic formulation that leads to our equations and introduce a bi-directional model where the organisms are allowed to change directions.


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P. A. Milewski. X. Yang. "A simple model for biological aggregation with asymmetric sensing." Commun. Math. Sci. 6 (2) 397 - 416, June 2008.


Published: June 2008
First available in Project Euclid: 1 July 2008

zbMATH: 1140.92018
MathSciNet: MR2433702

Primary: 35F25 , 35Q80 , 92D25 , 92D50

Keywords: chemotaxis , swarming , Traveling waves

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 2 • June 2008
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