Oscillatory behavior in a system of swarmalators with a short-range repulsive interaction

One of the computational models proposed to study emerging phenomena in decentralized systems is the swarmalator model [Nat. Commun. 8, 1504 (2017)2041-172310.1038/s41467-017-01190-3], where only long-range interactions are considered. But in living systems many of the collective behaviors observed arise from the combined effect of long- and short-range interactions. In this work we present an extension to the swarmalator model which includes a Gaussian short-range repulsive term of the type 1/σe^{-|x|^{2}/σ} along with the results of numerical simulations. Using several order parameters we can distinguish between static and dynamic aggregations and between synchronous and asynchronous states. We have found six long-term collective states, some of them not previously reported and the most remarkable one showing oscillatory collective behavior. The results obtained show a multiplicity of complex behaviors that extend the applicability of the swarmalator model.