We propose a self-propelled particle model for the swarming of
Daphnia that takes into account mutual repulsion and
attraction to a center. A vortex is formed only for a
range of propulsion strength, and vanishes for weak and strong
driving. The phase diagram and the
transitions between states with and without a vortex are analyzed,
and the nature of the phase boundaries is discussed based on a
linear stability analysis of the motion of individual swimmers. This
allows us to identify various key parameters determining the
characteristic features of the flow.
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