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We study the steady-state patterns of population of the coupled oscillatorsthat sync and swarm, where the interaction distances among oscillators havefinite-cutoff in interaction distance. We examine how the static patterns knownin the infinite-cutoff are reproduced or deformed, and explore a new staticpattern that does not appear until a finite-cutoff is considered. Allsteady-state patterns of the infinite-cutoff, static sync, static async, andstatic phase wave are respectively repeated in space for proper finite-cutoffranges. Their deformation in shape and density takes place for the otherfinite-cutoff ranges. Bar-like phase wave states are observed, which has notbeen the case for the infinite-cutoff. All the patterns are investigated vianumerical and theoretical analysis.

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