Swarmalator networks with multihop coupling.

Swarmalator systems intertwine two forms of collective behavior, swarming and synchronization, leading to the emergence of specific space-time patterns. Scaling the model to real-world phenomena and technical applications is problematic due to the assumption of global coupling among all swarmalators, which is impractical under physical constraints on interaction range. Conversely, purely local coupling was shown to be infeasible. To address this gap, we introduce and evaluate the concept of multihop coupling for swarmalators, which preserves the locality of physical interactions but propagates state information throughout the network via hop-limited and probabilistic flooding. It is demonstrated that convergence to the original emergent patterns can be achieved in a reliable and fast manner while keeping overhead low. A practical guideline for selecting the range, hop limit, and forwarding probability is provided. The range required for convergence can be approximated by the connectivity threshold of random geometric graphs.