Center for Complex and Nonlinear Science

A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czir\'ok et al. 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 dissussed and simulation of the ODEs presented.