A two-dimensional swarmalator system with Winfree-type phase coupling

Swarmalators—entities that combine spatial aggregation with phase oscillations—exhibit rich collective behaviours due to the interplay of spatial movement and phase dynamics. In this work, we study a system of swarmalators in two dimensions, where phase interactions follow the classical Winfree coupling framework. By systematically varying the coupling strength and natural frequency distribution, we uncover a diverse array of emergent states, including sync, phase wave and async states. Our analysis reveals how Winfree-type interactions influence self-organization, leading to novel dynamical regimes distinct from those observed with conventional Kuramoto-type coupling. We statistically analyse the spatial distributions of the emerging states and use them to study the phase dynamics semi-analytically.