Emergent behaviour of a generalized Viscek-type flocking model

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We present a planar agent-based flocking model with a distance-dependent communication weight. We derive a sufficient condition for the asymptotic flocking in terms of the initial spatial and heading-angle diameters and a communication weight. For this, we employ differential inequalities for the spatial and phase diameters together with the Lyapunov functional approach. When the diameter of the agent's initial heading-angles is sufficiently small, we show that the diameter of the heading-angles converges to the average value of the initial heading-angles exponentially fast. As an application of flocking estimates, we also show that the Kuramoto model with a connected communication topology on the regular lattice Z(d) for identical oscillators exhibits a complete-phase-frequency synchronization, when coupled oscillators are initially distributed on the half circle.
Publisher
IOP PUBLISHING LTD
Issue Date
2010-12
Language
English
Article Type
Article
Citation

NONLINEARITY, v.23, no.12, pp.3139 - 3156

ISSN
0951-7715
DOI
10.1088/0951-7715/23/12/008
URI
http://hdl.handle.net/10203/278725
Appears in Collection
MA-Journal Papers(저널논문)
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