Park Sung Min, Kim Beom Jun
Center of Complex Systems, Samsung Economic Research Institute, Seoul 140-702, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Aug;74(2 Pt 2):026114. doi: 10.1103/PhysRevE.74.026114. Epub 2006 Aug 18.
Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the Watts-Strogatz undirected network and then change undirected edges to directed arcs with a given probability, still preserving the connectivity of the network. A generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks. We observe that the directedness of complex networks plays an important role in emerging dynamical behaviors, which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks.
受真实生物神经元网络中大量定向突触耦合的启发，我们研究了定向网络中霍奇金 - 赫胥黎模型的同步行为。我们从瓦茨 - 斯托加茨无向网络的标准模型出发，然后以给定概率将无向边变为定向弧，同时仍保持网络的连通性。定义了一种用于定向网络的广义聚类系数，并用于研究定向网络的同步行为与潜在结构特性之间的相互作用。我们观察到复杂网络的定向性在新兴动力学行为中起着重要作用，这也通过对定向网络上的社会学博弈论选民模型的数值研究得到了证实。
