Synchronization in networks of chaotic systems with time-delay coupling

Toshiki Oguchi; Henk Nijmeijer; Takashi Yamamoto

doi:10.1063/1.2952450

Synchronization in networks of chaotic systems with time-delay coupling

Toshiki Oguchi, Henk Nijmeijer, Takashi Yamamoto

Dynamics and Control

Research output: Contribution to journal › Article › Academic › peer-review

62 Citations (Scopus)

Abstract

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 language	English
Article number	037108
Number of pages	14
Journal	Chaos
Volume	18
Issue number	3
DOIs	https://doi.org/10.1063/1.2952450
Publication status	Published - 22 Sep 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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abstract = "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.",

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AU - Oguchi, Toshiki

AU - Nijmeijer, Henk

AU - Yamamoto, Takashi

N1 - 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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Y1 - 2008/9/22

N2 - 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.

AB - 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.

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Synchronization in networks of chaotic systems with time-delay coupling

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