## 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.

Original language | English |
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Pages (from-to) | 62-68 |

Number of pages | 7 |

Journal | BioSystems |

Volume | 119 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 May |

Externally published | Yes |

## Keywords

- Collective behavior
- Metric distance
- Scale-free correlation
- Topological distance

## ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Applied Mathematics