Swarmalators with Stochastic Coupling and Memory

Swarmalators combine two types of distributed coordination - swarming and synchronization - whose mutual coupling leads to the emergence of spatio-temporal patterns. This paper studies issues for implementing swarmalators in the real world. First, the model is discretized in time to achieve limited communication overhead. We propose to apply stochastic coupling, in which entities broadcast their states at reduced rate, and introduce memory in each entity to store recently received state updates. The resulting system still converges to the original patterns. We investigate the convergence time and provide a lower limit for the rate of state exchange to ensure reasonable performance. Second, we show that inaccurate localization and physical size often have no impact on the pattern emergence, whereas limits for speed and acceleration lead to a slowdown. Our work is from the perspective of computing and robotics, but the approach and results can potentially be applied to other fields as well.