Synchronization in networks of chaotic systems with time-delay coupling

Toshiki Oguchi, Henk Nijmeijer, Takashi Yamamoto

Research output: Contribution to journalArticleAcademicpeer-review

62 Citations (Scopus)


In this paper, we consider synchronization of N identical nonlinear systems unidirectionally or bidirectionally coupled with time delay. First we show, using the small-gain theorem, that trajectories of coupled strictly semi-passive systems converge to a bounded region. Next, we consider the network structure under which the synchronization error dynamics has a trivial solution at zero and derive a necessary condition for synchronization with respect to the network structure. Using these facts, we then derive sufficient conditions for synchronization of the systems in terms of linear matrix inequalities via the Lyapunov-Krasovskii functional approach. The obtained results are illustrated on networks of Lorentz systems with coupling delay.

Original languageEnglish
Article number037108
Number of pages14
Issue number3
Publication statusPublished - 22 Sept 2008

Bibliographical note

Funding Information:
This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (No. 18560441).


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