K层层间单向耦合星形网络的同步能力分析

复杂网络是网络科学的一个研究热点。复杂网络同步能力的研究重点正从单层网络同步能力转向更加接近实际网络的多层有向网络同步能力。文章基于主稳定函数方法，深入研究4层层间单向耦合星形网络的特征值谱及其同步能力，给出了4层层间单向耦合星形网络的超拉普拉斯矩阵的特征值谱；在同步域有界和无界2种情况下，分析了K层层间单向耦合星形网络的同步能力与节点数、层数、层间耦合强度、层内耦合强度和中心节点耦合强度之间的关系；最后，通过数值仿真实验，讨论了K层层间单向耦合星形网络同步能力与各参数之间的关系（K =15）。

Analysis of Synchronization Ability of K Unidirectional Coupled Star Networks

Complex network is a hot spot in network science research. With the deepening of research, the research focus of complex network is shifting from single-layer network to multi-layer directed network closer to actual network. Based on the master stability function method, the eigenvalue spectrum and synchronization ability of the four-layer unidirectional coupled star network are studied. The eigenvalue spectrum of the supra-Laplace matrix of the four-layer unidirectional coupled star network is given. The relationship between the synchronization ability of the K layer unidirectional coupled star network and the node number, the number of layers, the intra-layer coupling strength and the inter-layer coupling strength are analyzed under the condition that the synchronization domain is bounded and unbounded. Finally, the simulation image of synchronization ability of K layer-by-layer unidirectional coupled star network is given（K=15）.