On forced swarmalators that move in higher-dimensional spaces

TL;DR

This paper extends the study of forced swarmalators from one-dimensional to higher-dimensional spaces, analyzing their dynamics, stability, and behaviors under sinusoidal forcing and power-law interactions.

Contribution

It introduces a higher-dimensional analysis of forced swarmalators, providing analytical characterizations and stability boundaries, and compares different interaction kernels.

Findings

Identification of higher-dimensional analogues of 1D states

Analytical characterization of dynamics and stability boundaries

Reproduction of complex behaviors with power-law interactions

Abstract

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.