Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Flocking and synchronization of particle models

Authors: Seung-Yeal Ha, Corrado Lattanzio, Bruno Rubino and Marshall Slemrod
Journal: Quart. Appl. Math. 69 (2011), 91-103
MSC (2000): Primary 92D25, 74A25, 76N10
DOI: https://doi.org/10.1090/S0033-569X-2010-01200-7
Published electronically: December 9, 2010
MathSciNet review: 2807979
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we present a multi-dimensional flocking model rigorously derived from a vector oscillatory chain model and study the connection between the Cucker-Smale flocking model and the Kuramoto synchronization model appearing in the statistical mechanics of nonlinear oscillators. We provide an alternative direct approach for frequency synchronization to the Kuramoto model as an application of the flocking estimate for the Cucker-Smale model.

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Additional Information

Seung-Yeal Ha
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: syha@snu.ac.kr

Corrado Lattanzio
Affiliation: Department of Pure and Applied Mathematics, University of L’Aquila, loc. Coppito, 67010 L’Aquila, Italy
Email: corrado.lattanzio@univaq.it

Bruno Rubino
Affiliation: Department of Pure and Applied Mathematics, University of L’Aquila, loc. Coppito, 67010 L’Aquila, Italy
Email: bruno.rubino@univaq.it

Marshall Slemrod
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Wisconsin 53706-1388
Email: slemrod@math.wisc.edu

DOI: https://doi.org/10.1090/S0033-569X-2010-01200-7
Keywords: Flocking, particles, mechanical model, synchronization
Received by editor(s): July 17, 2009
Published electronically: December 9, 2010
Article copyright: © Copyright 2010 Brown University

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