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Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise

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Abstract

This paper studies the outer synchronization of time delay complex networks of nonidentical topological structures in the presence of intrinsic time delay, time-varying coupling delay, and perturbation by noise. Considering one network as the drive network and the other as the response network, the drive-response networks achieve synchronization through a suitably designed adaptive controller. The stochastic LaSalle invariance principle is employed to theoretically prove the almost certain synchronization between two complex networks. The proposed controller is applicable to complex networks that have either intrinsic time delay or coupling delay or both. Two examples are examined to illustrate the proposed synchronization scheme and demonstrate its effectiveness.

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Acknowledgments

This research is supported by the National Foundation for Studying Abroad (2012), the Talents Project of Sichuan University of Science and Engineering (No. 2011RC07), the Key project of Artificial Intelligence Key Laboratory of Sichuan Province (No. 2011RZJ02), the Science and Technology Key Project of Zigong (No. 2012D09), the Cultivation Project of Sichuan University of Science and Engineering (No. 2012PY19), the High-level Innovative Talents Plan of Sichuan University of Science and Engineering (2014), and the Basic and Advanced Research Project of CQCSTC (No. cstc2014jcyjA00040).

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Authors and Affiliations

  1. School of Automatic and Electronic Information, Sichuan University of Science and Engineering, Zigong, 643000, China

    Da Lin

  2. Electrical Engineering Department, University of California, Los Angeles, Los Angeles, CA, 90095, USA

    Da Lin & Jia-Ming Liu

  3. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Fuchen Zhang

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  1. Da Lin
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  2. Jia-Ming Liu
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Correspondence to Da Lin.

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Lin, D., Liu, JM. & Zhang, F. Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise. Nonlinear Dyn 80, 117–128 (2015). https://doi.org/10.1007/s11071-014-1855-6

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  • DOI: https://doi.org/10.1007/s11071-014-1855-6

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