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Convergence for HRNNs with Unbounded Activation Functions and Time-varying Delays in the Leakage Terms

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Abstract

In this paper, the exponential convergence problems are considered for a class of high-order recurrent neural networks (HRNNs) with time-varying delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques. It is believed that these results are significant and useful for the design and applications of HRNNs. Even for the system without leakage delays, the criterion is shown to be different from a recent publication. Moreover, some examples are given to show the effectiveness of the proposed method and results.

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Acknowledgments

The authors would like to express the sincere appreciation to the reviewers for their helpful comments in improving the presentation and quality of the paper. In particular, the authors expresses the sincere gratitude to Prof. Bingwen Liu for the helpful discussion when this work is carried out. This work was supported by the National Natural Science Foundation of China (Grant no. 11201184), the Natural Scientific Research Fund of Hunan Provincial of China (Grant No. 11JJ6006), the Natural Scientific Research Fund of Hunan Provincial Education Department of PR China (Grant nos. 11C0916, 11C0915), the Natural Scientific Research Fund of Zhejiang Provincial of China (Grants nos. Y6110436, LY12A01018), and the Natural Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant no. Z201122436).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, 415000, Hunan, People’s Republic of China

    Renwei Jia

  2. Nanhu College, Jiaxing University, Jiaxing, 314001, Zhejiang, People’s Republic of China

    Mingquan Yang

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  1. Renwei Jia
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  2. Mingquan Yang
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Correspondence to Mingquan Yang.

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Jia, R., Yang, M. Convergence for HRNNs with Unbounded Activation Functions and Time-varying Delays in the Leakage Terms. Neural Process Lett 39, 69–79 (2014). https://doi.org/10.1007/s11063-013-9290-0

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  • DOI: https://doi.org/10.1007/s11063-013-9290-0

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