On forced swarmalators that move in higher-dimensional spaces

We study the collective dynamics of swarmalators subjected to periodic (sinusoidal) forcing. Although previous research focused on the simplified case of motion in a one-dimensional (1D) periodic domain, we extend this analysis to the more realistic scenario of motion in two and three spatial dimensions with periodic boundary conditions. In doing so, we identify analogues of the 1D states and characterize their dynamics and stability boundaries analytically. Additionally, we investigate the forced swarmalators model with power-law interaction kernels, finding that the analytically tractable model with periodic boundary conditions can reproduce the observed dynamic behaviors of this more complex model.