Tamura Koutarou, Takayasu Hideki, Takayasu Misako
Institute of Innovative Research, Tokyo Institute of Technology, 4259-S1-3, Nagatsuta-cho, Midori-ku, Yokohama, 226-8503, Japan.
Sony Computer Science Laboratories, 3-14-13, Higashigotanda, Shinagawa-ku, Tokyo, 141-0022, Japan.
Sci Rep. 2018 Apr 3;8(1):5517. doi: 10.1038/s41598-018-23675-x.
We analyzed nonlinear transport as defined for directed complex networks, where the flux from one node to a neighboring node is given preferentially according to the scalar quantities at the neighbor nodes. This is known as the generalized gravity interaction. In our research, we discovered a novel phase transition type. In the diffusion phase, the scalar quantity is scattered over the whole system, whereas in the localization phase, the flow tends to form localized confluence patterns owing to nonlinearity, resulting in the appearance of special nodes that irreversibly attract huge amounts of flow. We analytically considered the transition for selected network configurations, demonstrating that the transition point depends on the network topology. We also demonstrated that the diffusion phase of this transport model fits well with data from business firms, implying that the whole network structure can be used to model money flow in the real world.
我们分析了为有向复杂网络定义的非线性传输，其中从一个节点到相邻节点的通量优先根据相邻节点处的标量给出。这被称为广义引力相互作用。在我们的研究中，我们发现了一种新型的相变类型。在扩散阶段，标量散布在整个系统中，而在定位阶段，由于非线性，流倾向于形成局部汇流模式，导致出现不可逆地吸引大量流的特殊节点。我们通过分析考虑了选定网络配置的转变，证明转变点取决于网络拓扑。我们还证明了这种传输模型的扩散阶段与商业公司的数据拟合良好，这意味着整个网络结构可用于对现实世界中的资金流进行建模。
