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Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction–diffusion terms

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Abstract

The problem of mean square exponential stability for a class of impulsive stochastic fuzzy cellular neural networks with distributed delays and reaction–diffusion terms is investigated in this paper. By using the properties of M-cone, eigenspace of the spectral radius of nonnegative matrices, Lyapunov functional, Itô’s formula and inequality techniques, several new sufficient conditions guaranteeing the mean square exponential stability of its equilibrium solution are obtained. The derived results are less conservative than the results recently presented in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008). In fact, the systems discussed in Wang and Xu (Chaos Solitons Fractals 42:2713–2721, 2009), Zhang and Li (Stability analysis of impulsive stochastic fuzzy cellular neural networks with time varying delays and reaction–diffusion terms. World Academy of Science, Engineering and Technology 2010), Huang (Chaos Solitons Fractals 31:658–664, 2007), and Wang (Chaos Solitons Fractals 38:878–885, 2008) are special cases of ours. Two examples are presented to illustrate the effectiveness and efficiency of the results.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and constructive suggestions. This research is supported by the Natural Science Foundation of Guangxi Autonomous Region (No. 2012GXNSFBA053003), the National Natural Science Foundations of China (60973048, 60974025, 60673101, 60939003), National 863 Plan Project (2008 AA04Z401, 2009AA043404), the Natural Science Foundation of Shandong Province (No. Y2007G30), the Scientific and Technological Project of Shandong Province (No. 2007GG3WZ04016), the Science Foundation of Harbin Institute of Technology (Weihai) (HIT(WH)200807), the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF. 2001120), the China Postdoctoral Science Foundation (2010048 1000) and the Shandong Provincial Key Laboratory of Industrial Control Technique (Qingdao University).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, China

    Guowei Yang, Yonggui Kao, Wei Li & Sun Xiqian

  2. College of Information Engineering, Nanchang Hangkong University, Nanchang, 330063, China

    Guowei Yang

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  1. Guowei Yang
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  2. Yonggui Kao
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  3. Wei Li
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  4. Sun Xiqian
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Correspondence to Yonggui Kao.

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Yang, G., Kao, Y., Li, W. et al. Exponential stability of impulsive stochastic fuzzy cellular neural networks with mixed delays and reaction–diffusion terms. Neural Comput & Applic 23, 1109–1121 (2013). https://doi.org/10.1007/s00521-012-1040-0

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