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多层网络是当今网络科学研究的一个前沿方向。针对多层双向耦合星形网络的特征值谱对网络的同步能力进行了研究。通过严格推导出多层双向耦合星形网络特征值的解析表达式，分析了节点数、层数、层内耦合强度和层间耦合强度与网络同步能力的关系，重点分析了层数对网络同步能力的影响。网络的同步能力除了受层内耦合强度和层间叶子节点之间的耦合强度影响外，当同步域无界时，若层间叶子节点之间的耦合强度较弱，网络的同步能力还依赖于层数。当同步域有界时，网络的同步能力随节点数、层间中心节点之间的耦合强度增大而变弱；若层内耦合强度较弱，网络的同步能力随层数增大而减弱；若层间叶子节点之间的耦合强度较弱，网络的同步能力随层数增大反而增强。
Multi-layer network is a frontier direction of network science research. Aiming at the eigenvalue spectrum of multi-layer bidirectional coupled star network, the synchronization ability of the network is studied. By strictly deducing the analytical expression of eigenvalues of multi-layer bidirectional coupled star networks, the relationship between node number, number of layers, in-layer coupling strength and inter-layer coupling strength and network synchronization capability is analyzed. The relationship between layer number and network synchronization The impact of ability. In addition to the influence of coupling strength between layers and the coupling strength between leaf nodes, the synchronization ability of the network is not strong if the synchronization region is unbounded. If the coupling strength between leaf nodes is weak, the network synchronization ability also depends on the layer number. When the synchronization domain is bounded, the synchronization ability of the network becomes weaker with the increase of the node number and the coupling strength between the interlayer center nodes. If the in-layer coupling strength is weak, the network synchronization ability weakens with the increase of the number of layers; If the coupling between the leaf nodes is weak, the synchronization ability of the network increases with the increase of the number of layers.