Research Repository

Phase transitions in models of bird flocking

UNSPECIFIED (2014) 'Phase transitions in models of bird flocking.' In: UNSPECIFIED, (ed.) Chaos, Information Processing and Paradoxical Games: The Legacy of John S. Nicolis. UNSPECIFIED, 383 - 398. ISBN 9789814602136

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Abstract

© 2015 by World Scientific Publishing Co. Pte. Ltd. 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.

Item Type: Book Section
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 05 Dec 2016 14:37
Last Modified: 08 Jan 2019 12:15
URI: http://repository.essex.ac.uk/id/eprint/18339

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