Collective steady-state patterns of swarmalators with finite-cutoff interaction distance

We study the steady-state patterns of population of the coupled oscillators that sync and swarm, where the interaction distances among the oscillators have a finite-cutoff in the interaction distance. We examine how the static patterns known in the infinite-cutoff are reproduced or deformed and explore a new static pattern that does not appear until a finite-cutoff is considered. All steady-state patterns of the infinite-cutoff, static sync, static async, and static phase wave are repeated in space for proper finite-cutoff ranges. Their deformation in shape and density takes place for the other finite-cutoff ranges. Bar-like phase wave states are observed, which has not been the case for the infinite-cutoff. All the patterns are investigated via numerical and theoretical analyses.

Automated summary

This study investigates the steady-state patterns of population of coupled oscillators with a finite-cutoff in the interaction distance, revealing new static patterns that emerge only when a finite-cutoff is considered. Existing static patterns from infinite-cutoff, such as static sync, static async, and static phase waves, are repeated and deformed in space for different finite-cutoff ranges. Unique bar-like phase wave states are observed, presenting a deviation from the patterns seen in infinite-cutoff scenarios.