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

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