一般拓扑结构的复杂网络的稳定性和同步

Stability and Synchronization of Complex Networks with General Topology

研究了具有一般拓扑结构的复杂动态网络的稳定性和同步.相对于以往的复杂网络的稳定和同步研究,本文针对的是一般拓扑结构,即没有对外、内耦合矩阵进行限制.外耦合矩阵没有必要是对称阵或可对角化阵,内耦合矩阵也没有设定为对角阵或者正定阵.得到的主稳定方程包含外耦合矩阵和内耦合矩阵的谱信息,因此由其推导的稳定性和同步化条件和现有的结果相比更加精确和细致.最后的数值算例说明了结论的正确性.

This paper focuses on the stability and synchronization for complex dynamical networks with general topology. Compared to the previous work in the literature, the outer and inner coupling matrices of complex networks considered are ordinary ones without any restrictions,i, e. , the outer coupling matrix is not necessarily symmetric and the inner coupling matrix is not required to be diagonal or positive definite. The master stability equation （MSE） derived for complex networks contains the spectrum of both the outer and the inner matrices. Therefore, the conclusions evolved from the SME are more accurate than the previous results. Finally, a numerical example is given to illustrate the effectiveness of conclusions proposed.