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Square-mean almost periodic solution for stochastic Hopfield neural networks with time-varying delays on timescales

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Abstract

In this paper, we first propose a concept of square-mean almost periodic function on timescales. Then, by means of the fixed point theory and differential inequality techniques on timescales, we establish some sufficient conditions on the existence and global exponential stability of square-mean almost periodic solutions for a class of stochastic Hopfield neural networks with time-varying delays on timescales. Our results are new even if the timescale \({\mathbb {T}}={\mathbb {R}}\) or \({\mathbb {Z}}\). Finally, we present an example to illustrate our theoretical results.

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Acknowledgments

This work is supported by the National Natural Sciences Foundation of People’s Republic of China under Grant 11361072.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People’s Republic of China

    Yongkun Li

  2. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, Yunnan, People’s Republic of China

    Li Yang

  3. School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, 650091, Yunnan, People’s Republic of China

    Wanqin Wu

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  1. Yongkun Li
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  2. Li Yang
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  3. Wanqin Wu
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Correspondence to Yongkun Li.

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Li, Y., Yang, L. & Wu, W. Square-mean almost periodic solution for stochastic Hopfield neural networks with time-varying delays on timescales. Neural Comput & Applic 26, 1073–1084 (2015). https://doi.org/10.1007/s00521-014-1784-9

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  • DOI: https://doi.org/10.1007/s00521-014-1784-9

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