连接增加对网络同步能力的影响

Effect of increasing links on the synchronizability of network

文章运用矩阵理论,证明了无向网络对应耦合矩阵的第二大特征值随正耦合的增加(或加强)而不增这一性质。由耦合矩阵第二大特征值与网络同步能力之间的关系可知,同步区域无界的无向连通网络增加(或加强)正耦合后,其同步能力可能增强,也可能保持不变;增加(或加强)负耦合后,其同步能力可能降低,也可能保持不变。用几种具体网络验证了结果的正确性,数值计算结果表明,同步区域有界网络一般不具有这个性质。

Based on matrix theory, it is proved that the second largest eigenvalue of the coupling matrix which corresponds to undirected network maintains as the positive couplings increase or enhance. This property suggests that, if the positive （negative） couplings increase or enhance, synchronizability in a network with limitless synchronization region becomes stronger （weaker） or maintains. The validity of the result is illustrated by certain networks and the network with limited synchronization region usually does not possess the said property.