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Stability in distribution of stochastic delay recurrent neural networks with Markovian switching

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Abstract

This paper investigates the stability in distribution of stochastic delay recurrent neural networks with Markovian switching. Using Lyapunov function and stochastic analysis techniques, sufficient conditions on the stability in distribution are given. For such recurrent neural networks, it reveals that the limit distribution of transition probability for segment process associated with solution process is indeed a unique ergodic invariant probability measure. 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 Nos.11101054, 11272067, Hunan Provincial Natural Science Foundation of China under Grant No. 12JJ4005, the Scientific Research Funds of Hunan Provincial Education Department of China under Grant No.13C1036, Humanities and Social Sciences Foundation of Ministry of Education of China under Grants No. 12YJAZH173 and the National Social Science Foundation of China under Grant No.15BJY12.

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410004, Hunan, People’s Republic of China

    Enwen Zhu

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

    George Yin

  3. Department of Mathematics, Statistics and Computer Science, University of Wisconsin-Stout, Menomonie, WI, 54751, USA

    Quan Yuan

Authors
  1. Enwen Zhu
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  2. George Yin
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  3. Quan Yuan
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Correspondence to Enwen Zhu.

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Zhu, E., Yin, G. & Yuan, Q. Stability in distribution of stochastic delay recurrent neural networks with Markovian switching. Neural Comput & Applic 27, 2141–2151 (2016). https://doi.org/10.1007/s00521-015-2013-x

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  • DOI: https://doi.org/10.1007/s00521-015-2013-x

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