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Outer synchronization of complex networks with delay via impulse

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Abstract

Synchronization between the driving network and the responding network (outer synchronization) has attracted increasing attention from various fields of science and engineering. In this paper, we address outer synchronization of complex networks with delays. Both the cases of coupling delay and node delay are considered. Employing the impulsive control method which is simple, efficient, low cost, and easy to implement in practical applications, we obtain some sufficient conditions of outer synchronization. It indicates that outer synchronization can be achieved if the maximal impulsive intervals are less than a critical value. Numerical simulations are also given to demonstrate the effectiveness of the proposed impulsive control scheme.

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Acknowledgements

The work is supported by the National Nature Science Foundation of China (No. 70571059) and Young Project (Q20111309) and Key Program (D20101304) of Hubei Provincial Department of Education.

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Authors and Affiliations

  1. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, P.R. China

    Wen Sun & Zhong Chen

  2. Institute of Systems Science Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Wen Sun & Jinhu Lü

  3. College of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China

    Shihua Chen

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  1. Wen Sun
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  2. Zhong Chen
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  3. Jinhu Lü
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  4. Shihua Chen
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Correspondence to Wen Sun.

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Sun, W., Chen, Z., Lü, J. et al. Outer synchronization of complex networks with delay via impulse. Nonlinear Dyn 69, 1751–1764 (2012). https://doi.org/10.1007/s11071-012-0383-5

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  • DOI: https://doi.org/10.1007/s11071-012-0383-5

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