  We study the collective behavior of swarmalators, generalizations of phase
oscillators that both sync and swarm, confined to move on a 1D ring. This
simple model captures some of the essence of movement in 2D or 3D but has the
benefit of being solvable: most of the collective states and their bifurcations
can be specified exactly. The model also captures the behavior of real-world
swarmalators which swarm in quasi-1D rings such as bordertaxic sperm and
vinegar eels.
