Stability Analysis of Flock and Mill rings for 2nd Order Models in Swarming

We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. We relate the instability of the flock rings wit...

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Bibliographic Details
Published in:arXiv.org 2013-04
Main Authors: Albi, G, Balagué, D, Carrillo, J A, J von Brecht
Format: Article
Language:English
Subjects:
Biological models (mathematics)
Clustering
Stability
Stability analysis
Swarming
Online Access:Get full text
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Summary:We study the linear stability of flock and mill ring solutions of two individual based models for biological swarming. The individuals interact via a nonlocal interaction potential that is repulsive in the short range and attractive in the long range. We relate the instability of the flock rings with the instability of the ring solution of the first order model. We observe that repulsive-attractive interactions lead to new configurations for the flock rings such as clustering and fattening formation. Finally, we numerically explore mill patterns arising from this kind of interactions together with the asymptotic speed of the system.
ISSN:2331-8422