Analysis of dynamically stable patterns in a maze-like corridor using the Wasserstein metric

The two-dimensional optimal velocity (2d-OV) model represents a dissipative system with asymmetric interactions, thus being suitable to reproduce behaviours such as pedestrian dynamics and the collective motion of living organisms. In this study, we found that particles in the 2d-OV model form optimal patterns in a maze-like corridor. Then, we estimated the stability of such patterns using the Wasserstein metric. Furthermore, we mapped these patterns into the Wasserstein metric space and represented them as points in a plane. As a result, we discovered that the stability of the dynamical patterns is strongly affected by the model sensitivity, which controls the motion of each particle. In addition, we verified the existence of two stable macroscopic patterns which were cohesive, stable, and appeared regularly over the time evolution of the model.