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FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

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Acta Mathematica Scientia 2024年第2期44卷 632-649页

作者：金春银李双智 College of Science China Agricultural UniversityBeijing100083China

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

关键词： flocking local interaction thermodynamical Cucker-Smale model stochastic matrix neighbor graph

Connectivity and synchronization of Vicsek model

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Science in China(Series F) 2008年第7期51卷 848-858页

作者： LIU ZhiXin GUO Lei Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China

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.

关键词： Vicsek model synchronization stochastic matrix connectivity neighbor graph

Unsupervised Linear Discriminant Analysis

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Journal of Shanghai Jiaotong university(Science) 2006年第1期11卷 40-42页

作者：唐宏方涛施鹏飞唐国安 Inst.of Image Processing & Pattern Recognition Shanghai Jiaotong Univ Shanghai 200030 China Three Gorges Project Command of Armed Police Hydropower Eng.Troops Hubei 443133

An algorithm for unsupervised linear discriminant analysis was presented. Optimal unsupervised discriminant vectors are obtained through maximizing covariance of all samples and minimizing covariance of local k-neares... 详细信息

关键词： linear discriminant analysis(LDA) unsupervised learning neighbor graph

How Many Leaders Are Required for Consensus

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How Many Leaders Are Required for Consensus