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Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller

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Abstract

This paper discusses the synchronization problem for a class of reaction–diffusion neural networks with Dirichlet boundary conditions. Unlike other studies, a sampled-data controller with stochastic sampling is designed in order to synchronize the concerned neural networks with reaction–diffusion terms and time-varying delays, where \(m\) sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. A novel discontinuous Lyapunov–Krasovskii functional with triple integral terms is introduced based on the extended Wirtinger’s inequality. Using Jensen’s inequality and reciprocally convex technique in deriving the upper bound for the derivative of the Lyapunov–Krasovskii functional, some new synchronization criteria are obtained in terms of linear matrix inequalities. Numerical examples are provided in order to show the effectiveness of the proposed theoretical results.

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Acknowledgments

The work of the first author was supported by NBHM Research Project; Quanxin Zhu’s work was jointly supported by the National Natural Science Foundation of China (61374080), the Natural Science Foundation of Zhejiang Province (LY12F03010), the Natural Science Foundation of Ningbo (2012A610032), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, Tamilnadu, India

    R. Rakkiyappan & S. Dharani

  2. School of Mathematical Sciences, Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Quanxin Zhu

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  1. R. Rakkiyappan
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  2. S. Dharani
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  3. Quanxin Zhu
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Correspondence to Quanxin Zhu.

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Rakkiyappan, R., Dharani, S. & Zhu, Q. Synchronization of reaction–diffusion neural networks with time-varying delays via stochastic sampled-data controller. Nonlinear Dyn 79, 485–500 (2015). https://doi.org/10.1007/s11071-014-1681-x

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  • DOI: https://doi.org/10.1007/s11071-014-1681-x

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