Connectivity and synchronization of Vicsek model
Connectivity and synchronization of Vicsek model
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DOI：
10.1007/s11432-008-0077-2
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发表时间：
2008-06
期刊：
影响因子：
--
通讯作者：
Zhixin Liu;Lei Guo
中科院分区：
文献类型：
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作者：
Zhixin Liu;Lei Guo
多智能体系统的集体行为是复杂系统研究的一个重要内容，Vicsek模型是多智能体系统的一个基本模型，它具有复杂系统的一些关键特征，如动态行为、局部相互作用、邻域变化等。Jadbabaie等人分析了该模型中的线性化航向方程，并表明所有智能体最终都会同步，前提是与智能体位置相关的邻居图满足一定的连通性条件。自Jadbabaie的工作发表以来，许多后续的研究工作都致力于Vicsek模型的分析。然而，一个尚未解决的关键问题是，当这样的连接是满意的。本文给出了Vicsek模型同步的一个充分条件，该条件只对模型参数施加。此外，通过反例证明了当初始航向在[0，2 π）内时，相邻图的连通性不足以使Vicsek模型同步，从而揭示了Vicsek模型与其线性化模型的根本区别.
The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents’ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie’s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0, 2π), which reveals some fundamental differences between the Vicsek model and its linearized version.