Effects of coupling range on the dynamics of swarmalators

We study a variant of the one-dimensional swarmalator model where the units' interactions have a controllable length scale or range. We tune the model from the long-range regime, which is well studied, into the short-range regime, which is insufficiently studied, and find diverse collective states: sync dots, where the swarmalators arrange themselves into k>1 delta points of perfect synchrony; q-waves, where the swarmalators form spatiotemporal waves with winding number q>1; and an active state where unsteady oscillations are found. We present the phase diagram and derive most of the threshold boundaries analytically. These states may be observable in real-world swarmalator systems with low-range coupling, such as biological microswimmers or active colloids.