Atay Fatihcan M, Biyikoğlu Türker
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jul;72(1 Pt 2):016217. doi: 10.1103/PhysRevE.72.016217. Epub 2005 Jul 25.
The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved. Similarly, adding links to a network may worsen its synchronizability, although it decreases the average distance in the graph.
研究了图操作对耦合动力系统同步性的影响。这些操作范围从链路的添加或删除到组合网络以及从简单网络生成更大网络的各种方式。利用图论方法计算或估计拉普拉斯算子的特征值，这些特征值决定了在网络上演化的连续或离散时间动力学的同步性。研究结果用于解释对随机、无标度和小世界网络的数值观测。一个有趣的特征是，当通过在两个网络之间添加链路来组合它们时，所得网络的同步性可能会变差，尽管各个网络的同步性得到了改善。同样，向一个网络添加链路可能会使其同步性变差，尽管这会减小图中的平均距离。
