Mixed sign interactions in the 1D swarmalator model

We study a population of swarmalators, mobile variants of phase oscillators, which run on a ring and have mixed sign interactions. This 1D swarmalator model produces several of collective states: the standard sync and async states as well as a novel splay-like "polarized" state and several unsteady states such as active bands or swirling. The model's simplicity allows us to describe some of the states analytically. The model can be considered as a toy model for real-world swarmalators such as vinegar eels and sperm which swarm in quasi-1D geometries.