Self-organized circling, clustering and swarming in populations of chiral swarmalators

Chiral swarmalators are active particles with intrinsic dynamical chirality that exhibit persistent rotational motion in space. Collaborative spatial swarming behaviors emerge when chiral swarmalators with heterogeneous chiralities are coupled in an alignment rule. In this paper, we extensively studied the self-organized swarming dynamics of populations of spatially non-interacting chiral swarmalators with phase coupling from the viewpoint of nonlinear dynamics and synchronization. Chiral synchronization dynamics plays important role in adapting spatial swarming behaviors. By modulating the coupling strength and scope, swarmalators may organize into coordinated circlings, spatial clusterings, and other swarming patterns. Chirality-induced phase separations of circling and cluster patterns are revealed, which obeys the interesting rule of “like chiralities attract, while opposite chiralities repel”. The formation mechanism and transitions of these various swarming patterns are explored, and the phase diagrams are given. Critical boundaries separating various collective states are analytically derived. These miscellaneous ordered swarming patterns are shown to be robust to parameter heterogeneity and stochastic noises. The present paves an avenue of the pattern formation and swarming dynamics of interacting chiral agents.