Stigmergic feedback in swarmalator mixtures: Phase-mediated segregation under confinement

In this study, we explore self-organization in a two-dimensional swarm model composed of two distinct swarmalator types (A and B) with opposing angular velocities,  focusing on the roles of stigmergy-mediated interactions, phase-dependent motion, and physical constraints, including boundary conditions and barrier effects. Unlike  raditional approaches that rely on local or direct physical interactions, the proposed swarm coordinates through internal phase-based dynamics coupled with environmental phase modifications. The intrinsic angular velocity of each swarmalator determines its phase rotation, which in turn governs its orbital motion and phase interactions with the environment. The non-equilibrium simulations reveal varying degrees of segregation across different segregation stages, observed across different time horizons, which are quantified by pairwise measures of neighborhood homogeneity specific to swarmalator type (A or B). Co-rotating pairs (AA or BB) channel trajectories via stigmergy, forming uniform clusters of the same type. In contrast, counter-rotating pairs (AB or BA) induce phase mixing, cluster decay, and fluctuations
at cluster peripheries. At high stigmergy-mediated coupling, dynamic ring-shaped clusters emerge, with their macroscopic rotation direction determined by the sign of the angular velocity. Our findings underscore the importance of the interplay between indirect interactions and spatial constraints in shaping emergent self-organized patterns. This work provides a blueprint for constructing bioinspired robotic systems that adapt through environmental feedback, paving the way for advanced environments designed to actively guide swarm behaviors.