Fluctuation-driven flocking movement in three dimensions and scale-free correlation.

Takayuki Niizato,Yukio-Pegio Gunji

doi:10.1371/journal.pone.0035615

Abstract

Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of “topological distances” and “scale-free correlations” are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the “metric distance”). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations.

Highlights

Much has been learned about collective behavior from both experimental and theoretical studies [1,2,3,4,5,6,7,8,9]
The emergence of global coherence in groups, for example, can be described in terms of the following density-dependent property: locusts and fish tend to move as a collective when their density reaches a certain level [1,2]. These density-dependent collective phenomena can be well explained by the self-propelled particle (SPP) model proposed by Vicsek et al The SPP model is commonly used to explain collective behavior [11,12,13], and it consists of two rules: (1) each individual in two-dimensional space has a neighborhood with an interaction radius, and (2) each individual attempts to match its direction to the average of the other individuals in the neighborhood, modified by external noise
We proposed a new flocking model, the metric-topological interaction (MTI) model, that accounts for recent empirical observations

Summary

Introduction

Much has been learned about collective behavior from both experimental and theoretical studies [1,2,3,4,5,6,7,8,9]. The emergence of global coherence in groups, for example, can be described in terms of the following density-dependent property: locusts and fish tend to move as a collective when their density reaches a certain level [1,2] These density-dependent collective phenomena can be well explained by the self-propelled particle (SPP) model proposed by Vicsek et al The SPP model is commonly used to explain collective behavior [11,12,13], and it consists of two rules: (1) each individual in two-dimensional space has a neighborhood with an interaction radius, and (2) each individual attempts to match its direction to the average of the other individuals in the neighborhood, modified by external noise. These three interaction ranges make flocking behavior more dynamic and sometimes produce nontrivial properties in the flocking movement, such as collective memory [16]

Methods

Results

Conclusion