Du Juan, Ma Xiujuan, Ma Fuxiang, Yu Wenqian
School of Computer Science, Qinghai Normal University, Xining, 810000, Qinghai, China.
The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Xining, 810016, Qinghai, China.
Sci Rep. 2024 Mar 13;14(1):6125. doi: 10.1038/s41598-024-56198-9.
Hyper-networks tend to perform better in representing multivariate relationships among nodes. Yet, due to the complexity of the hyper-network structure, research in synchronization dynamics is rarely involved. In this paper, a Kuramoto model more suitable for k-uniform hyper-networks is proposed. And the generalized Laplacian matrix expression of the k-uniform hyper-network is present. We use the eigenvalue ratio of the generalized Laplacian matrix to quantify synchronization. And we studied the effects of some important structure parameters on the synchronization of three types of k-uniform hyper-networks. And obtained different relationships between synchronization and these parameters. The results show the synchronization of the k-uniform hyper-networks is related to both structure and parameters. And as the size of the nodes increases, the synchronization ability gradually increases for ER random hyper-network, while that gradually decreases for NW small-world hyper-network and BA scale-free hyper-network. As the uniformity increases, the synchronization ability of all three types of uniform hyper-networks increases. In addition, when the structure and node size are fixed, the synchronization ability increases with the increase of the hyper-clustering coefficient in BA scale-free hyper-network and ER random hyper-network, while it decreases with the increase of the hyper-clustering coefficient in NW small-world hyper-network.
超网络在表示节点之间的多元关系方面往往表现得更好。然而，由于超网络结构的复杂性，同步动力学方面的研究很少涉及。本文提出了一种更适合k - 均匀超网络的Kuramoto模型。并且给出了k - 均匀超网络的广义拉普拉斯矩阵表达式。我们使用广义拉普拉斯矩阵的特征值比来量化同步。并且研究了一些重要结构参数对三种类型的k - 均匀超网络同步的影响。并得到了同步与这些参数之间的不同关系。结果表明，k - 均匀超网络的同步与结构和参数都有关系。并且随着节点规模的增加，ER随机超网络的同步能力逐渐增强，而NW小世界超网络和BA无标度超网络的同步能力逐渐减弱。随着均匀性的增加，所有三种类型的均匀超网络的同步能力都增强。此外，当结构和节点规模固定时，BA无标度超网络和ER随机超网络的同步能力随着超聚类系数的增加而增强，而NW小世界超网络的同步能力随着超聚类系数的增加而减弱。
