A Model of Scale-Free Proportion Based on Mutual Anticipation

Abstract

Recently, new empirical research of flocking behavior has been accumulated. Scale-free proportion has revealed how a flock can appear to behave as if it has one mind and body. The notion of scale-free proportion implies that the correlated domain within a flock is not constant size, but is proportional to flock size. Scale-free proportion can be explained by previous models, such as BOIDS based on the fixed radius neighborhood where an agent interacts with others if the critical valued parameter and a huge neighborhood are given. However, it is hard to explain under the normal neighborhood condition. The authors propose a new computational model that, although also based on BOIDS, incorporates mutual anticipation, which is implemented by modeling the resonance between the potential transitions available to each agent, allowing overlap between them. Via mutual anticipation, this model implements interactions not only among individuals but also between individuals and the field. The authors show that this model reveals the dynamic and robust structure of a flock or swarm, as well as scale-free proportion over a wide range of the flock sizes, comparing previous models, and that its predictions correlate well with empirical field data.