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W 1,2(Ω)- and X 1,2(Ω)-stability of reaction-diffusion cellular neural networks with delay

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Abstract

With Poincare’s inequality and auxiliary function applied in a class of retarded cellular neural networks with reaction-diffusion, the conditions of the systems’ W 1,2(Ω)-exponential and X 1,2(Ω)-asmptotic stability are obtained. The stability conditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end.

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Authors and Affiliations

  1. Hunan Institute of Engineering, Xiangtan, 411101, China

    YiPing Luo, WenHua Xia & GuoRong Liu

  2. Institute of System Engineering, South China University of Technology, Guangzhou, 510640, China

    YiPing Luo & FeiQi Deng

Authors
  1. YiPing Luo
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  2. WenHua Xia
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  3. GuoRong Liu
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  4. FeiQi Deng
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Correspondence to YiPing Luo.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60374023), the Natural Science Foundation of Hunan Province (Grant No. 07JJ6112), and Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 04A012 and 07A015), and the Construct Program of the Key Discipline in Hunan Province (Control Theory and Control Engineering)

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Luo, Y., Xia, W., Liu, G. et al. W 1,2(Ω)- and X 1,2(Ω)-stability of reaction-diffusion cellular neural networks with delay. Sci. China Ser. F-Inf. Sci. 51, 1980–1991 (2008). https://doi.org/10.1007/s11432-008-0139-5

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  • DOI: https://doi.org/10.1007/s11432-008-0139-5

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