Non-local interactions in collective motion

• Main Authors: Arthur E. B. T. King, Matthew S. Turner
• Format: Article
• Language: English
• Published: The Royal Society 2021-03-01
• Series: Royal Society Open Science
• Subjects: self-propelled particles; flocking; self-organization; collective dynamics; collective motion; swarming
• Online Access: https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.201536

The collective motion of animal groups often exhibits velocity–velocity correlations between nearest neighbours, with the strongest velocity correlations observed at the shortest inter-animal spacings. This may have been a motivational factor in the development of models based primarily on short-ranged interactions. Here we ask whether such observations necessarily mean that the interactions are short-ranged. We develop a minimal model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counterexample: the strongest velocity correlations emerge at the shortest distances, even when the interactions are explicitly non-local.