Janus Oscillators that Sync and Swarm

Swarmalators exhibit spatial and temporal self-organization; agents’ motions depend on their phase interactions and their phase behavior depends on their relative positions. The coupling between their spatial dynamics and phase dynamics leads to diverse emergent collective behaviors similar to a wide variety of collective systems. Past work in the swarmalator field has considered mobile phase oscillators that couple to each other through a single internal phase; in this work we demonstrate that when agents exhibit two phases and have a dipole geometry, their pairwise interactions enable a wide variety of emergent collective behaviors resembling those of Janus matchsticks, electro-active colloids, and phototactic micromotors, among many others. Through this work we introduce the Janus swarmalators, which open the door to studying the emergent behaviors of systems made up of particles that have components with incompatible physical and chemical properties like magnetic, electrical, or optical properties that enable the collective to exhibit synergistic functions. We characterize the self-organized behaviors across a parameter space of spatial and phase coupling variables and distinguish between many of the states through several order parameters. We study a small fraction of the large parameter space this model opens up, and find many states with diverse spatiotemporal self-organization; we pick two of the most surprising dynamic states and analyze the mechanisms through which they occur. Our Janus swarmalator framework represents a major thrust in self-organization phenomena that could aid in the characterization and development of future microrobot swarms for programmable self-assembly and active matter.