Scale-free correlations, influential neighbours and speed control in flocks of birds

Charlotte K. Hemelrijk*, Hanno Hildenbrandt

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)563-578
Number of pages16
JournalJournal of Statistical Physics
Issue number3
Early online date6-Dec-2014
Publication statusPublished - Feb-2015


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

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