Scaling Mobility Patterns and Collective Movements: Deterministic Walks in Lattices

Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey. Scaling laws in the displacement distribution emerge when the amount of prey resource approaches the critical point. Around the critical point, our model generates ordered collective movements of walkers with a quasi-periodic synchronization of walkers' directions. These results indicate that the co-evolution of walkers' least-action behavior and the landscape could be a potential origin of not only the individual scaling mobility patterns, but also the flocks of animals. Our findings provide a bridge to connect the individual scaling mobility patterns and the ordered collective movements.