Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies
Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies
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DOI：
10.1142/s0219530520500025
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发表时间：
2020-05
影响因子：
2.2
通讯作者：
Jiu‐Gang Dong;Seung‐Yeal Ha;Doheon Kim
中科院分区：
文献类型：
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作者：
Jiu‐Gang Dong;Seung‐Yeal Ha;Doheon Kim
研究了具有开关网络拓扑结构的热力学Cucker-Smer(TCS)模型的涌现动力学。TCS模型是一种具有额外内动力变量的广义CS模型，称为“温度”，其中等温情况与CS模型完全一致。在以往的研究中，TCS模型的涌现动力学大多局限于一些静态的网络拓扑结构，如完全图、每个结点具有正进出度的连通图和具有生成树的有向图。本文考虑了时间块序列中具有生成树的交换网络拓扑结构，并根据初始数据和系统参数给出了导致渐近单簇簇聚的两个充分框架。在第一个框架中，时间块的大小由某个正常数一致有界，我们证明了温度和速度直径以指数形式快速趋于零，空间直径是一致有界的。在第二个框架中，我们承认时间块的大小可以通过对数函数温和增长的情况。在后一个框架中，我们的温度和速度直径趋向于零，至少代数缓慢。
We study the emergent dynamics of the thermomechanical Cucker–Smale (TCS) model with switching network topologies. The TCS model is a generalized CS model with extra internal dynamical variable called “temperature” in which isothermal case exactly coincides with the CS model for flocking. In previous studies, emergent dynamics of the TCS model has been mostly restricted to some static network topologies such as complete graph, connected graph with positive in and out degrees at each node, and digraphs with spanning trees. In this paper, we consider switching network topologies with a spanning tree in a sequence of time-blocks, and present two sufficient frameworks leading to the asymptotic mono-cluster flocking in terms of initial data and system parameters. In the first framework in which the sizes of time-blocks are uniformly bounded by some positive constant, we show that temperature and velocity diameters tend to zero exponentially fast, and spatial diameter is uniformly bounded. In the second framework, we admit a situation in which the sizes of time-blocks may grow mildly by a logarithmic function. In latter framework, our temperature and velocity diameters tend to zero at least algebraically slow.