title: Emergence of the scale-invariant proportion in a flock from the metric-topological interaction.
abstract: Recently, it has become possible to more precisely analyze flocking behavior. Such research has prompted a reconsideration of the notion of neighborhoods in the theoretical model. Flocking based on topological distance is one such result. In a topological flocking model, a bird does not interact with its neighbors on the basis of a fixed-size neighborhood (i.e., on the basis of metric distance), but instead interacts with its nearest seven neighbors. Cavagna et al., moreover, found a new phenomenon in flocks that can be explained by neither metric distance nor topological distance: they found that correlated domains in a flock were larger than the metric and topological distance and that these domains were proportional to the total flock size. However, the role of scale-free correlation is still unclear. In a previous study, we constructed a metric-topological interaction model on three-dimensional spaces and showed that this model exhibited scale-free correlation. In this study, we found that scale-free correlation in a two-dimensional flock was more robust than in a three-dimensional flock for the threshold parameter. Furthermore, we also found a qualitative difference in behavior from using the fluctuation coherence, which we observed on three-dimensional flocking behavior. Our study suggests that two-dimensional flocks try to maintain a balance between the flock size and flock mobility by breaking into several smaller flocks.
authors.affiliation: Faculty of Engineering, Information and Systems, Tsukuba University, Japan. Electronic address: t_niizato@yahoo.co.jp.
authors.forename: Takayuki
authors.initials: T
authors.lastname: Niizato
authors.affiliation: Graduate School of Science, Kobe University, Japan.
authors.forename: Hisashi
authors.initials: H
authors.lastname: Murakami
authors.affiliation: Graduate School of Science, Kobe University, Japan; Faculty of Science, Kobe University, Japan.
authors.forename: Yukio-Pegio
authors.initials: YP
authors.lastname: Gunji
mesh_terms: D000818:Animals; D001522:Behavior, Animal / Q000502:physiology*; D001717:Birds / Q000502:physiology*; D003198:Computer Simulation; D005426:Flight, Animal / Q000502:physiology*; D008399:Mass Behavior; D008954:Models, Biological
keywords: Collective behavior; Metric distance; Scale-free correlation; Topological distance