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Exponential convergence for HRNNs with continuously distributed delays in the leakage terms

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Abstract

This paper considers exponential convergence for a class of high-order recurrent neural networks (HRNNs) with continuously distributed delays in the leakage terms (i.e., “leakage delays”). 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, which are new and complement previously known results. In particular, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed delays in the leakage terms. Moreover, an example is given to show the effectiveness of the proposed method and results.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant no. 11201184), the Hunan Provincial Natural Science Foundation of China(12JJ3007), the Natural Scientific Research Fund of Zhejiang Provincial of China (Grant no. LY12A01018), and the Natural Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant no. Z201122436). 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.

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Correspondence to Mingquan Yang.

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Chen, Z., Yang, M. Exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Comput & Applic 23, 2221–2229 (2013). https://doi.org/10.1007/s00521-012-1172-2

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  • DOI: https://doi.org/10.1007/s00521-012-1172-2

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