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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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References

  1. Cao J, Wang J (2005) Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuits Syst-I 52(5):920–931

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst-I 52(2):417–426

    Article  MathSciNet  MATH  Google Scholar 

  3. Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A 8(48):1015–1026

    Article  MathSciNet  MATH  Google Scholar 

  4. Balasubramaniam P, Nagamani G (2012) Global robust passivity analysis for stochastic fuzzy interval neural networks with time-varying delays. Expert Syst Appl 39(1):732–742

    Article  Google Scholar 

  5. Duan L, Huang L, Fang X (2017) Finite-time synchronization for recurrent neural networks with discontinuous activations and time-varying delays. Chaos 27(1):013101

    Article  MathSciNet  MATH  Google Scholar 

  6. Li H, Lam J, Cheung KC (2012) Passivity criteria for continuous-time neural networks with mixed time-varying delays. Appl Math Comput 218:11062–11074

    MathSciNet  MATH  Google Scholar 

  7. Gargi R, Chaba Y, Patel RB (2012) Improving the performance of dynamic source routing protocal by optimization of neural networks. Int J Math Sci Iss 9(4):471–479

    Google Scholar 

  8. Liu B (2016) Global exponential convergence of non-autonomous cellular neural networks with multi-proportional delays. Neurocomputing 191:352–355

    Article  Google Scholar 

  9. Liu B (2017) Finite-time stability of a class of CNNs with heterogeneous proportional delays and oscillating leakage coefficients. Neural Process Lett 45:109–119

    Article  Google Scholar 

  10. Yu Y (2017) Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett 45:141–151

    Article  Google Scholar 

  11. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cyber 8:1323–1331

    Article  Google Scholar 

  12. Liu B (2017) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Methods Appl Sci 40:167–174

    Article  MathSciNet  MATH  Google Scholar 

  13. Yu Y (2016) Global exponential convergence for a class of neutral functional differential equations with proportional delays. Math Methods Appl Sci 39:4520–4525

    Article  MathSciNet  MATH  Google Scholar 

  14. Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1–7

    MathSciNet  MATH  Google Scholar 

  15. Yao L (2017) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett 45:401–409

    Article  Google Scholar 

  16. Yao L (2018) Global convergence of CNNs with neutral type delays and \(D\) operator. Neural Comput Appl 29:105–109

    Article  Google Scholar 

  17. Zhang A (2017) Pseudo almost periodic solutions for neutral type SICNNs with \(D\) operator. J Exp Theor Artif Intell 29(4):795–807

    Article  Google Scholar 

  18. Farina L, Rinaldi S (2000) Positive linear systems: theory and applications. Wiley, New York

    Book  MATH  Google Scholar 

  19. Smith H (2008) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. American Mathematical Society, Providence

    Book  Google Scholar 

  20. Liu X, Yu W, Wang L (2010) Stability analysis for continuous time positive systems with time-varying delays. IEEE Trans Autom Control 55(4):1024–1028

    Article  MathSciNet  MATH  Google Scholar 

  21. Zaidi I, Chaabane M, Tadeo F, Benzaouia A (2015) Static state feedback controller and observer design for interval positive systems with time delay. IEEE Trans Circuits Syst-II 62(5):506–510

    Article  Google Scholar 

  22. Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9(3):830–841

    Article  MathSciNet  MATH  Google Scholar 

  23. Lu W, Chen T (2007) \(R^{n}_{+}\)-global stability of a Cohen-Grossberg neural network system with nonnegative equilibria. Neural Netw 20(6):714–722

    Article  MATH  Google Scholar 

  24. Berman A, Plemmons RJ (1979) Nonnegative matrices in the mathematical science. Academic Press, New York

    MATH  Google Scholar 

  25. Smith HL (1995) Monotone dynamical systems. Mathematical Surveys Monography American Mathematical Society, Providence

    Google Scholar 

  26. Le Van Hien (2017) On global exponential stability of positive neural networks with time-varying delay. Neural Netw 87:22–26

    Article  Google Scholar 

  27. Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl https://doi.org/10.1007/s00521-016-2558-3,1-19

  28. M’hamdi MS, Touati A (2016) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):1–20

    MathSciNet  Google Scholar 

  29. Mhamdi MS, Cao J, Alsaedi A (2017) piecewise pseudo almost periodic solution for impulsive generalised high-order hopfield neural networks with leakage delays. Neural Process Lett. 45(2):615–648

    Article  Google Scholar 

  30. Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodyn 10(6):1–19

    Article  MathSciNet  Google Scholar 

  31. Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260:378–392

    Article  Google Scholar 

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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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