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New Results on Exponential Convergence for HRNNs with Continuously Distributed Delays in the Leakage Terms

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Abstract

This paper concerns with exponential convergence for a class of high-order recurrent neural networks with continuously distributed delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of the networks converge exponentially to the zero point by using Lyapunov functional method and differential inequality techniques, which correct some recent results of Chen and Yang (Neural Comput Appl. doi:10.1007/s00521-012-1172-2, 2012). Moreover, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed leakage delays.

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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. This research was supported by Science Fund for Distinguished Young Scholars of Zhejiang Province of China (Grant no. R1100002), the Natural Scientific Research Fund of Hunan Provincial of China (Grant no. 11JJ6006), and the Natural Scientific Research Fund of Hunan Provincial Education Department of China (Grant nos. 11C0916 and 11C0915).

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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

    Yuehua Yu

  2. College of Engineering, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Weidong Jiao

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  1. Yuehua Yu
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  2. Weidong Jiao
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Correspondence to Weidong Jiao.

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Yu, Y., Jiao, W. New Results on Exponential Convergence for HRNNs with Continuously Distributed Delays in the Leakage Terms. Neural Process Lett 39, 167–177 (2014). https://doi.org/10.1007/s11063-013-9296-7

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  • DOI: https://doi.org/10.1007/s11063-013-9296-7

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