An ODE model of the motion of pelagic fish

被引：32
作者：
Birnir, Bjoern [1 ]
机构：
[1] Univ Calif Santa Barbara, Ctr Complex & Nonlinear Sci, Santa Barbara, CA 93106 USA
[2] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
来源：
JOURNAL OF STATISTICAL PHYSICS | 2007年 / 128卷 / 1-2期
关键词：
collective motion; fish schools; migration; periodic solutions; tori; stability; equivariant bifurcation theory; swarming; structural stability; heteroclinic orbits;
D O I：
10.1007/s10955-007-9292-2
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirok et at. [Phys. Rein Lett. 75(6):1226-1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic, are discussed and simulation of the ODEs presented.
引用
收藏
页码：535 / 568
页数：34
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