E61 Emergent group dynamics

Topic

The group dynamics of an insect swarm—specifically the type of swarm that exemplifies this class of models—emerge from simple local interaction rules; these rules give rise to complex collective behavior without the need for a central leader.

The Vicsek model describes this emergent process: each individual in the swarm tends to align its direction of movement with the average direction of its neighbors within a specific interaction radius, subject to a certain level of noise.

The Vicsek model demonstrates a phase transition between a disordered swarm state (characterized by low density or high noise) and an ordered collective state (characterized by high density or low noise), a transition analogous to the magnetic transition found in the Ising model.

The order parameter in this model quantifies the degree of coordination within the swarm. Consequently, this model—characterized by the leaderless, emergent group dynamics with which it began—causes the swarm of midges (or the bee swarm, which establishes a similar model) to exhibit both a long-range velocity correlation that decays quite slowly and a giant number fluctuation that scales significantly with the total number of individuals in the swarm. This suggests that the swarm operates near a critical point that maximizes its collective response to a specific perturbation. As the swarm moves even closer to this critical point, its collective response to a perturbation becomes even faster, thereby reinforcing the leaderless, emergent group dynamics that defined the model at the outset.

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