Flocking by stopping: a novel mechanism of emergent order in collective movement

Abstract

Collective movement is observed widely in nature, where individuals interact locally to produce globally ordered, coherent motion. In typical models of collective motion, each individual takes the average direction of multiple neighbors, resulting in ordered movement. In small flocks, noise induced order can also emerge with individuals copying only a randomly chosen single neighbor at a time. We propose a new model of collective movement, inspired by how real animals move, where individuals can move in two directions or remain stationary. We demonstrate that when individuals interact with a single neighbor through a novel form of halting interaction -- where an individual may stop upon encountering an oppositely moving neighbor rather than instantly aligning -- persistent collective order can emerge even in large populations. This represents a fundamentally different mechanism from conventional averaging-based or noise-induced ordering. Using deterministic and stochastic mean-field approximations, we characterize the conditions under which such ``flocking by stopping'' behavior can occur, and confirm the mean-field predictions using individual-based simulations. Our results highlight how incorporating a stopped state and halting interactions can generate new routes to order in collective movement.