TY - JOUR

T1 - Emergence of the scale-invariant proportion in a flock from the metric-topological interaction

AU - Niizato, Takayuki

AU - Murakami, Hisashi

AU - Gunji, Yukio Pegio

PY - 2014/5

Y1 - 2014/5

N2 - 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.

AB - 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.

KW - Collective behavior

KW - Metric distance

KW - Scale-free correlation

KW - Topological distance

UR - http://www.scopus.com/inward/record.url?scp=84899982080&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899982080&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2014.03.001

DO - 10.1016/j.biosystems.2014.03.001

M3 - Article

C2 - 24686118

AN - SCOPUS:84899982080

VL - 119

SP - 62

EP - 68

JO - Currents in modern biology

JF - Currents in modern biology

SN - 0303-2647

IS - 1

ER -