Phase Transitions in Models of Bird Flocking

Abstract

The aim of the present paper is to elucidate the transition from collective to random behavior exhibited by various mathematical models of bird flocking. In particular, we compare Vicsek's model [Viscek et al., Phys. Rev. Lett. 75, 1226 -- 1229 (1995)] with one based on topological considerations. The latter model is found to exhibit a first order phase transition from flocking to decoherence, as the 'noise parameter' of the problem is increased, whereas Viscek's model gives a second order transition. Refining the topological model in such a way that birds are influenced mostly by the birds in front of them, less by the ones at their sides and not at all by those behind them (because they do not see them), we find a behavior that lies in between the two models. Finally, we propose a novel mechanism for preserving the flock's cohesion, without imposing artificial boundary conditions or attracting forces.

11 pages, 6 figures, To appear in the special volume honoring the memory of Professor John S. Nicolis, Chaos, Information Processing and Paradoxical Games, World Scientific Publishing Company, 2014, edited by G. Nicolis and V. Basios

References in corpus (5)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Relevance of Metric-Free Interactions in Flocking Phenomena
• Emergence of coherent motion in aggregates of motile coupled maps