STABILITY ANALYSIS OF FLOCK AND MILL RINGS FOR SECOND ORDER MODELS IN SWARMING

Authored by G Albi, D Balague, Josa A Carrillo, Brecht J Von

Date Published: 2014

DOI: 10.1137/13091779x

Sponsors: Generalitat de Catalunya Royal Society United Kingdom Engineering and Physical Sciences Research Council (EPSRC) United States National Science Foundation (NSF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

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 clustering and fattening instabilities for flock rings that prove analogous to similar instabilities that occur for ring solutions of the first order model. Finally, we numerically explore mill patterns arising from these interactions by varying the asymptotic speed of the system.

Tags

Simulation Dynamics collective behavior Aggregation System Self-driven particles Continuum-limit Fish schools