Phase Transitions in Models of Bird Flocking

Christodoulidi, H, van der Weele, K., Antonopoulos, Ch.G. and Bountis, T. (2015) Phase Transitions in Models of Bird Flocking. In: Chaos, Information Processing and Paradoxical Games. World Scientific, pp. 383-398. ISBN UNSPECIFIED

Full content URL: http://doi.org/10.1142/9789814602136_0019

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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 [Vicsek 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 Vicsek’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 attractive forces.

Keywords:Active matter, synchronization, collective behavior, Phase transitions
Subjects:G Mathematical and Computer Sciences > G120 Applied Mathematics
G Mathematical and Computer Sciences > G150 Mathematical Modelling
F Physical Sciences > F340 Mathematical & Theoretical Physics
Divisions:College of Science > School of Mathematics and Physics
ID Code:37016
Deposited On:16 Sep 2019 10:06

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