Swarmalator collectives with phase lag under resonant and non-resonant forcing

We investigate the collective dynamics of two-dimensional swarmalators under both resonant and non-resonant forcing. We examine forced swarmalator dynamics with homogeneous and heterogeneous phase lag parameters in both spatial and phase variables. In particular, we demonstrate how the interplay between the phase lag and the forcing strength governs the emergent dynamics of the swarmalator collectives. As a result, we identify several novel collective states, including active coherent states, breathing flow states, persistent directional order states, directionally synchronized core states, irregular pulsating states, and intermittent directional order states. In addition, we also observe active phase-wave states, asynchronous states, phase-locked states, active chimera states, and global translational motion states, which are characterized using appropriate order parameters and the Euclidean distance. We find that the critical strength of the forcing required for the transition to the phase-locked state is higher for the repulsive coupling than for the attractive coupling in both resonant and non-resonant forcing. For the non-resonant forcing, the system exhibits consistent collective behavior in the phase diagram at low forcing strengths, whereas in the resonant case, large variations in collective states emerge even at very small forcing strengths. We further analyze the evolution of the collective states under heterogeneous phase lag for both resonant and non-resonant forcing. Finally, we derive analytical stability conditions for the phase-locked state, which show agreement with the numerical results. These findings provide insight into collective dynamics governed by nonreciprocal interactions and external forcing with potential applications in engineering and robotic systems.