Dynamics of swarmalators in the presence of a contrarian

Swarmalators--agents that simultaneously exhibit spatial swarming and phase synchronization--serve as a powerful framework for exploring collective behavior in complex systems. We study a two-dimensional swarmalator model perturbed by a predator-like agent, termed the contrarian, which influences both the positions and internal phases of the swarmalators. This coupling leads to the emergence of rich dynamical patterns, including clustering, phase synchronization with negative coupling, and novel collective states. Remarkably, we observe that strong interactions with the contrarian can induce global phase coherence even when direct swarmalator coupling is repulsive. Using a combination of analytical techniques and numerical simulations, we map out the transitions between distinct collective behaviors as system parameters are varied. These results highlight how antagonistic or out-of-phase influences can paradoxically enhance coherence in coupled spatial-phase systems.