•   •   •   •

Download the Paper (1.8 MB, PDF file) - January 24, 2008 Tell a colleague about it. Printing Tips: Select 'print as image' in the Acrobat print dialog if you have trouble printing.

ABSTRACT:
In this paper, we study simulations of the schooling and swarming behavior of a mathematical model for the motion of pelagic fish. We use a derivative of a discrete model of interacting particles originated by Vicsek, Czir´ok et al. [6] [5] [23] [24]. Recently, a system of ODEs was derived from this model [2], and using these ODEs, we find transitory and long-term behavior of the discrete system. In particular, we numerically find stationary, migratory, and circling behavior in both the discrete and the ODE model and two types of swarming behavior in the discrete model. The migratory solutions are numerically stable and the circling solutions are metastable. We find a stable circulating ring solution of the discrete system where the fish travel in opposite directions within an annulus. We also find the origin of noise-driven swarming when repulsion and attraction are absent and the fish interact solely via orientation.

SUGGESTED CITATION:
Alethea Barbaro, Kirk Taylor, Peterson F. Trethewey, Lamia Youseff, and Bjorn Birnir, "Discrete and continuous models of the dynamics of pelagic fish: application to the capelin" (January 24, 2008). Center for Complex and Nonlinear Science. Paper Bio3.
http://repositories.cdlib.org/cnls/Bio3