Flocking by stopping: A mechanism of emergent order in collective movement

In typical models of collective motion, each individual takes the average direction of multiple neighbors, resulting in the ordered movement of large flocks. Alternatively, interactions with only one random neighbor at a time can also lead to order, referred to as noise-induced order, but only in small flocks. Here, we propose a new model of collective movement in which individuals interact with a single random neighbor yet can produce order in large flocks. Our model consists of individuals who can also stop, inspired by the intermittent stop-and-go motion in real animals. We introduce a halting interaction in which an individual may stop upon encountering a neighbor moving in the opposite direction, rather than instantly aligning. Using mean-field deterministic and stochastic approximations for a one-dimensional version of the model, we show that persistent collective order emerges even in large flocks. This represents a different mechanism from conventional averaging-based order in large flocks or noise-induced ordering in small flocks. We confirm the mean-field predictions using individual-based simulations in both one and two dimensions. Our results highlight how incorporating a stopped state and halting interactions can generate new routes to order in collective movement.