An ODE Model of the Motion of Pelagic Fish |
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Authors: | Björn Birnir |
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Affiliation: | (1) Center for Complex and Nonlinear Science and Department of Mathematics, University of California, Santa Barbara, USA |
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Abstract: | A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. 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. |
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Keywords: | Collective motion fish schools migration periodic solutions tori stability equivariant bifurcation theory swarming structural stability heteroclinic orbits |
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