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Journal of Statistical Physics

, Volume 158, Issue 3, pp 563–578 | Cite as

Scale-Free Correlations, Influential Neighbours and Speed Control in Flocks of Birds

  • Charlotte K. HemelrijkEmail author
  • Hanno Hildenbrandt
Article

Abstract

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.

Keywords

Flocks of birds Self-organization Number of influential neighbours Spatial dynamics Scale-free correlation Speed control Information transmission 

Notes

Acknowledgments

We are grateful for the grants that have been supporting this research, Hemelrijk’s Startup Grant of her Rosalind Franklin Fellowship and her Grant in the European Project of the 7th framework, StarFlag for the work by Hanno Hildenbrandt. We thank the self-organization group for regular discussions.

Supplementary material

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Behavioural Ecology and Self-Organisation, Centre for Ecological and Evolutionary StudiesUniversity of GroningenGroningenThe Netherlands

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