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

被引：49

作者：

Albi, G. ^{[1
]}

Balague, D. ^{[2
]}

Carrillo, J. A. ^{[3
]}

Von Brecht, J. ^{[4
]}

机构：

[1] Univ Ferrara, Dipartimento Matemat & Informat, I-44121 Ferrara, Italy

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[4] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2014年 / 74卷 / 03期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

swarming; interacting particles; stability of solutions; dynamical systems; SELF-DRIVEN PARTICLES; COLLECTIVE BEHAVIOR; CONTINUUM-LIMIT; FISH SCHOOLS; AGGREGATION; SIMULATION; DYNAMICS; SYSTEM;

D O I：

10.1137/13091779X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：794 / 818

页数：25

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