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Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays

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Abstract

This paper presents some new results on the existence, uniqueness and generalized exponential stability of a positive equilibrium for positive recurrent neural networks with multi-proportional delays. Based on the differential inequality techniques, a testable condition is established to guarantee that all solutions of the considered system converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.

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Acknowledgements

The author would like to express the sincere appreciation to the editor and reviewers for their helpful comments in improving the presentation and quality of the paper. In particular, the author expresses the sincere gratitude to Prof. Jianying Shao (Jiaxing University, Zhejiang) for the helpful discussion when this revision work was being carried out. This work was supported by National Social Science Fund of China (Grant No. 15BJY122), Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2016JJ6103, 2016JJ6104), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY18A010019), and Natural Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 17C1076).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan, People’s Republic of China

    Gang Yang

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  1. Gang Yang
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Correspondence to Gang Yang.

Additional information

Supported by National Social Science Fund of China(Grant No. 15BJY122), Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2016JJ6103, 2016JJ6104), Zhejiang Provincial Natural Science Foundation of China (Grant No. LY18A010019), and Natural Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 17C1076).

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Yang, G. Exponential Stability of Positive Recurrent Neural Networks with Multi-proportional Delays. Neural Process Lett 49, 67–78 (2019). https://doi.org/10.1007/s11063-018-9802-z

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  • DOI: https://doi.org/10.1007/s11063-018-9802-z

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