Delay-induced transitions in swarmalator clusters

We investigate the role of delay in the collective dynamics of swarmalators introduced recently by O’Keeffe, Hong, and Strogatz. Addition of delay into the system of swarmalators was motivated by the biology of early embryonic development. The delay leads to a rich phenomenology, which includes two new collective states. In one of them, all particles in a swarm execute decaying radial oscillations completely in phase with each other. After these oscillations decay, the swarm becomes a static quasi-crystal. We call this the “breathing” state. The other collective state is one in which particles close to the surface of the swarm execute non-decaying convective motions. We call it the “surface boiling” state. For a range of negative phase coupling strengths, there is a transition from the boiling to the breathing state as delay time is increased.