期刊
NONLINEARITY
卷 23, 期 12, 页码 3139-3156出版社
IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/23/12/008
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资金
- Korea government(MEST) [2009-0093137]
- SNU-CNS
- National Research Foundation of Korea [2009-0093137] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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.
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