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pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

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Abstract

This paper investigates the problem of the pth moment exponential stability for a class of stochastic recurrent neural networks with Markovian jump parameters. With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, some novel sufficient conditions on the pth moment exponential stability of the considered system are derived. The results obtained in this paper are completely new and complement and improve some of the previously known results (Liao and Mao, Stoch Anal Appl, 14:165–185, 1996; Wan and Sun, Phys Lett A, 343:306–318, 2005; Hu et al., Chao Solitions Fractals, 27:1006–1010, 2006; Sun and Cao, Nonlinear Anal Real, 8:1171–1185, 2007; Huang et al., Inf Sci, 178:2194–2203, 2008; Wang et al., Phys Lett A, 356:346–352, 2006; Peng and Liu, Neural Comput Appl, 20:543–547, 2011). Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants No.11101054,11272067, Hunan Provincial Natural Science Foundation of China under Grant No.12JJ4005 and the Scientific Research Funds of Hunan Provincial Science and Technology Department of China under Grants No.2012SK3096.

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410004, Hunan, China

    Enwen Zhu

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Quan Yuan

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  1. Enwen Zhu
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  2. Quan Yuan
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Correspondence to Enwen Zhu.

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Zhu, E., Yuan, Q. pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching. Neural Process Lett 38, 487–500 (2013). https://doi.org/10.1007/s11063-013-9297-6

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