Effect of spatial-phase drift on the synchronization of swarmalators with higher-order interactions

The synchronization of complex networks is a fundamental phenomenon with significant implications across physics, biology, and neuroscience. While pairwise interactions have been extensively studied, higher-order interactions, which capture dependencies among multiple nodes, remain underexplored despite their critical role in real-world systems. Furthermore, in real-world networks, node variables such as spatial positions and phases can exhibit delays or drifts, introducing additional complexity to synchronization dynamics. This study investigates the impact of spatial-phase drift on synchronization transitions in a swarmalator model with both first-order and second-order interactions. Using the Ott-Antonsen framework for analytical derivations, supported by numerical simulations, we demonstrate that spatial-phase drift can either suppress or enhance synchronization transitions depending on coupling conditions. Increasing spatial-phase drift reduces the bistable region and transition region, leading to smoother and more continuous transitions. This work provides theoretical insights into the interplay between coupling structures and drifts, advancing our understanding of synchronization in networks with higher-order interactions. Swarmalators, phase oscillators that swarm around in space and synchronize in time, have been used to model behaviors of real-world systems like vinegar eels or magnetic domain walls. This study investigates the role of spatial-phase delay on the synchronization of swarmalators with higher-order interactions.