带参数的外耦合矩阵对网络聚类数目的影响

摘要

For a relationship between the network dynamics characteristics and the weight of element in the matrix,the effect of the outer-coupling matrix with parameter on the number of cluster in a network with four nodes is investigated.Based on matrix theory,the threshold value of coupling strength and the parameter for clustering bifurcation of network have been obtained by calculating the maximal eigenvalue of the transverse space corresponding to the invariant manifolds of the network.The research shows that the synchronization state will come into being cluster bifurcation with the change of the parameter ηand the coupling strength ε.Numerical simulations in the Chua circuit verify the theoretical results.%针对矩阵中元素的权重与网络动力学特征的关系,研究了带参数的外耦合矩阵对具有4个节点的网络聚类数目的影响.基于矩阵理论,通过计算网络不变流形对应的横截空间的最大特征值,得到了网络产生聚类分岔时的参数阈值.研究表明,随着参数η和耦合强度ε的改变,网络的同步态会产生聚类分岔现象.以Chua电路进行数值模拟,验证了理论结果的正确性.