Belykh Igor, Belykh Vladimir, Hasler Martin
Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.
Chaos. 2006 Mar;16(1):015102. doi: 10.1063/1.2146180.
We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have equal input and output weight sums. We obtain the same upper bound for synchronization in asymmetrically connected networks as in the network with a symmetrized matrix, provided that the condition of node balance is satisfied. In terms of graphs, the symmetrization operation amounts to replacing each directed edge by an undirected edge of half the coupling strength. It should be stressed that without node balance this property in general does not hold.
我们研究极限环或混沌振子的非对称连接网络中同步的全局稳定性。我们将连接图稳定性方法扩展到具有节点平衡的有向图，即网络中所有节点的输入和输出权重总和相等的特性。只要满足节点平衡条件，我们就能得到非对称连接网络中同步的上界，与具有对称化矩阵的网络相同。从图的角度来看，对称化操作相当于用耦合强度减半的无向边替换每个有向边。需要强调的是，没有节点平衡，这个特性通常不成立。
