Nonlinear Dynamics

, Volume 86, Issue 1, pp 489–499 | Cite as

Theoretical analysis of synchronization in delayed complex dynamical networks with discontinuous coupling

  • Yongzheng Sun
  • Zhicai Ma
  • Feng Liu
  • Jie Wu
Original Paper


In this paper, we study the synchronization problem of time-delayed complex networks with discontinuous coupling. Sufficient conditions for the synchronization are obtained based on the stability theory of differential equations. The theoretical results show that the time-delayed networks can achieve synchronization even if the coupling is switched off sometimes. We find analytically that the speed of synchronization is proportional to the on–off rate of the coupling and the algebraic connectivity of networks. Finally, the analytical results are confirmed by numerical simulations.


Complex network Synchronization Time delay 



We thank the anonymous referees for their helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11226150 and 61403393), the Fundamental Research Funds for the Central Universities (Grant No. 2015XKMS076), and the China Scholarship Council (Grant No. 201308320087).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of SciencesChina University of Mining and TechnologyXuzhouPeople’s Republic of China
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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