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Almost periodic solution of impulsive Hopfield neural networks with finite distributed delays

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Abstract

By the definition of piecewise almost periodic functions, this paper investigates the existence and stability of a discontinuous almost periodic solution of the impulsive Hopfield neural networks with finite distributed delays and periodic impulses, using fixed point theorems, Lyapunov functional, and some inequality techniques. Compared with known relevant results mainly concentrating on continuous neural networks, the obtained criteria consider impulse effects. Moreover, it does not use Cauchy matrix, and the corresponding hypotheses about linear impulse systems which are often used in the reference. The obtained criteria are easily applicable and checkable, and an illustrative example with simulations shows this. Furthermore, the proposed results are applicable to some other networks with periodic impulses.

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Acknowledgments

This work is supported by NCET under Grant NCET-08-0370, SRFDP under Grants 20090181110052, and Projects of International Cooperation and Exchanges, Sichuan Province under Grant 2010HH0031, all from China.

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Authors and Affiliations

  1. Vision and Image Processing Laboratory, School of Computer Science and Engineering, Sichuan University, 610064, Chengdu, People’s Republic of China

    Yiguang Liu, Zengxi Huang & Liping Chen

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  1. Yiguang Liu
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  2. Zengxi Huang
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  3. Liping Chen
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Correspondence to Yiguang Liu.

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Liu, Y., Huang, Z. & Chen, L. Almost periodic solution of impulsive Hopfield neural networks with finite distributed delays. Neural Comput & Applic 21, 821–831 (2012). https://doi.org/10.1007/s00521-011-0655-x

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  • DOI: https://doi.org/10.1007/s00521-011-0655-x

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