Li Zhi
Department of Automatic Control Engineering, Xidian University, P.O. Box 136, Xi'an 710071, China.
Chaos. 2008 Jun;18(2):023124. doi: 10.1063/1.2931332.
Based on the original definition of the synchronization stability, a general framework is presented for investigating the exponential stability of synchronization in asymmetrically coupled networks. By choosing an appropriate Lyapunov function, we prove that the mechanism of the exponential synchronization stability is the asymmetrical coupling matrix with diffusive condition. We deduce the second largest eigenvalue of a symmetric matrix to govern the exponential stability of synchronization in asymmetrically coupled networks. Moreover, we have given the threshold value which can guarantee that the states of the asymmetrically coupled network achieve the exponential stability of synchronization.
基于同步稳定性的原始定义，提出了一个用于研究非对称耦合网络中同步指数稳定性的通用框架。通过选择合适的李雅普诺夫函数，我们证明了指数同步稳定性的机制是具有扩散条件的非对称耦合矩阵。我们推导了一个对称矩阵的第二大特征值来控制非对称耦合网络中同步的指数稳定性。此外，我们给出了能够保证非对称耦合网络状态实现同步指数稳定性的阈值。
