Master Stability Equations of Complex Dynamical Networks with General Topology
Master Stability Equations of Complex Dynamical Networks with General Topology
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DOI：
10.3182/20080706-5-kr-1001.00264
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
Hongfei Sun;D. Hill
中科院分区：
文献类型：
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作者：
Hongfei Sun;D. Hill
得到了一类具有一般拓扑结构的复杂动态网络的主稳定性方程。与之前的工作相比，我们几乎消除了网络图上的所有限制。耦合构型矩阵不一定是可对角化的，耦合系数不一定是非负的，网络图可以是有向的。这些新的主稳定性方程与以前的研究一样，在分析复杂动态网络与流形同步的稳定性方面仍然是非常有效的。我们提出了一些关于稳定性的新观察。提出了一个新的概念“重连通”，它可以看作是对无向图的“连通”和对有向图的“强连通”的推广。这两个主要定理的证明很短，但可以代替文献中的许多证明。
Abstract The master stability equations for a complex dynamical network with general topology are obtained. Compared to prior work, we remove almost all the restrictions on the graph of the network. The coupling configuration matrix is not necessarily diagonalizable, the coupling coefficients are not necessarily nonnegative, and the graph of the network can be directed. These new master stability equations as for those in the previous studies are still very effective in analyzing the stability of complex dynamical networks in terms of synchronization to a manifold. We present some new observations on stability. A new concept “heavily connected”, which can be regarded as the generalization of both “connected” for an undirected graph and “strong connected” for a directed graph, is proposed. The proofs of the two main theorems are very short but can substitute many of those in the literature.