Chinese Annals of Mathematics, Series B

, Volume 28, Issue 6, pp 737–746

Exponential Synchronization of the Linearly Coupled Dynamical Networks with Delays*


DOI: 10.1007/s11401-006-0194-4

Cite this article as:
Liu, X. & Chen, T. Chin. Ann. Math. Ser. B (2007) 28: 737. doi:10.1007/s11401-006-0194-4


In this paper, the authors investigate the synchronization of an array of linearly coupled identical dynamical systems with a delayed coupling. Here the coupling matrix can be asymmetric and reducible. Some criteria ensuring delay-independent and delay-dependent global synchronization are derived respectively. It is shown that if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronization stability of the network will be restrained, even eventually de-synchronized.


Time-delaySynchronizationExponential stabilityLeft eigenvector

2000 MR Subject Classification


Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Laboratory of Nonlinear Mathematics Science, School of Mathematical SciencesFudan UniversityShang-haiChina
  2. 2.Laboratory of Nonlinear Mathematics Science, School of Mathematical SciencesFudan UniversityShanghaiChina