Swarmalators with delayed interactions

TL;DR

This paper studies how delays in interactions affect the collective behavior of swarmalators, revealing two distinct steady states with unique spatial and motion patterns, similar to phenomena observed in colloids and biological systems.

Contribution

It introduces the effects of delayed interactions in swarmalator models, identifying new steady states and dynamic behaviors not previously characterized.

Findings

Identification of a motionless pseudo-crystalline disk state

Discovery of a boiling state with convective motions near the boundary

Analogies to behaviors in colloids and biological systems

Abstract

We investigate the effects of delayed interactions in a population of ``swarmalators", generalizations of phase oscillators that both synchronize in time and swarm through space. We discover two steady collective states: a state in which swarmalators are essentially motionless in a disk arranged in a pseudo-crystalline order, and a boiling state in which the swarmalators again form a disk, but now the swarmalators near the boundary perform boiling-like convective motions. These states are reminiscent of the beating clusters seen in photoactivated colloids and the living crystals of starfish embryos.