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首页> 外文期刊>Journal of Statistical Physics >Scale-Free Correlations, Influential Neighbours and Speed Control in Flocks of Birds
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Scale-Free Correlations, Influential Neighbours and Speed Control in Flocks of Birds

机译：鸟群的无标度相关性，影响邻居和速度控制

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Coordination of birds in large flocks is amazing, especially, since individual birds only interact with a few neighbors (the so-called 'influential neighbours'). Yet, empirical data show that fluctuations of velocity and speed of different birds are correlated beyond the influential neighbours and are correlated over a larger distance in a larger flock. This correlation between the correlation length of velocity or speed and flock size was found to be linear, called a scale-free correlation. It depends on the way individuals interact in the flock, for instance, on the number of influential neighbours and speed control. It is unknown however, how exactly the number of influential neighbours affects this scale-free correlation. Recent empirical data show that different degrees of control of speed affect the scale-free correlation for speed fluctuations. Theoretically, based on statistical mechanics, it is predicted that at very high speed control, the correlation is no longer scale-free but saturates at a certain correlation length and this hampers coordination in flocks. We study these issues in a model, called StarDisplay, because its behavioural rules are biologically inspired and many of its flocking patterns resemble empirical data. Our results show that the correlation length of fluctuations of velocity as well as speed correlate with flock size in a scale-free manner. A higher number of influential neighbours causes a diminishing increase of the slope of the scale-free correlation with velocity, resulting thus in flocks that coordinate more uniformly. Similar to recent empirical data higher speed control reduces the correlation length of speed fluctuations in our model. As predicted theoretically, at very high speed control the model generates a non-scale free correlation, and although there are still flocks, they are in the process of disintegrating.
机译：大型鸡群中的鸟类协调是惊人的，特别是因为单个鸟类只与少数几个邻居（所谓的“有影响力的邻居”）互动。然而，经验数据表明，不同禽类的速度和速度波动与有影响的邻居之间相关，并且与较大鸡群中的较大距离相关。发现速度或速度的相关长度与羊群大小之间的这种相关是线性的，称为无标度相关。它取决于个人在羊群中的互动方式，例如，有影响力的邻居的数量和速度控制。但是，尚不清楚影响邻居的数量究竟如何影响这种无标度关联。最新的经验数据表明，不同程度的速度控制会影响速度波动的无标度相关性。从理论上讲，基于统计力学，可以预见，在非常高的速度控制下，相关不再不再是无标度的，而是在一定的相关长度处达到饱和，这会妨碍群中的协调。我们在名为StarDisplay的模型中研究这些问题，因为其行为规则受到生物学启发，并且其许多植绒模式都类似于经验数据。我们的结果表明，速度波动的相关长度以及速度以无标度的方式与羊群大小相关。较大数量的有影响力的邻域会导致无标度相关性的斜率随速度的增加而减小，从而导致群更均匀地协调。与最近的经验数据相似，更高的速度控制可减小模型中速度波动的相关长度。正如理论上所预测的那样，在极高的速度控制下，该模型会生成无标度的自由相关性，尽管仍然存在羊群，但它们仍在分解中。

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