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Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays

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Abstract

This article investigates the passivity of reaction–diffusion genetic regulatory networks (GRNs) with time-varying delays and uncertainty terms under Dirichlet, Neumann, and Robin boundary conditions. We provide delay-dependent stability criteria by constructing appropriate Lyapunov–Krasovskii functions and linear matrix inequalities, and offer conditions sufficient to ensure the passivity of GRNs. We conducted a comparative analysis of GRNs under these three conditions. Numerical examples of the proposed approaches are provided to illustrate its effectiveness, and represent the three-dimensional figures of the trajectories of the concentrations of mRNA and the proteins of GRNs under Dirichlet boundary conditions.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61425002, 61672121, 61572093, 61402066, 61402067, 61370005, 31370778, 61672124, 61370145, 61173183), the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_15R07), the Program for Liaoning Innovative Research Team in University (No. LT2015002), the Basic Research Program of the Key Lab in Liaoning Province Educational Department (Nos. LZ2014049, LZ2015004), Scientific Research Fund of Liaoning Provincial Education (Nos. L2015015, L2014499), and the Program for Liaoning Key Lab of Intelligent Information Processing and Network Technology in University.

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Chengye Zou, Xiaopeng Wei & Qiang Zhang

  2. Key Laboratory of Advanced and Intelligent Computing, Dalian University, Ministry of Education, Dalian, 116622, China

    Qiang Zhang & Changjun Zhou

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  1. Chengye Zou
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  2. Xiaopeng Wei
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  3. Qiang Zhang
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  4. Changjun Zhou
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Correspondence to Xiaopeng Wei or Qiang Zhang.

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Zou, C., Wei, X., Zhang, Q. et al. Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays. Neural Process Lett 47, 1115–1132 (2018). https://doi.org/10.1007/s11063-017-9682-7

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  • DOI: https://doi.org/10.1007/s11063-017-9682-7

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