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Global Lagrange stability for neutral type neural networks with mixed time-varying delays

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Abstract

In this paper, the global exponential stability in Lagrange sense for neutral type neural networks with mixed time-varying delays is studied. By constructing proper Lyapunov functions and using inequality techniques, new delay-dependent succinct criteria are derived to ensure the global exponential Lagrange stability for the aforementioned neural networks. Meanwhile, globally exponentially attractive sets are given out. The results obtained here are more general than some of existing results. Finally, two examples are presented and analyzed to validate our results.

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References

  1. Dhamala M, Jirsa V, Ding M (2004) Enhancement of neural synchrony by time delay. Physical Rev Lett 92(074104):1–4

    Google Scholar 

  2. Chua L, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circ Syst 35(10):1257–1272

    Article  MathSciNet  MATH  Google Scholar 

  3. Xu S, Lam J (2006) A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Networks 19(1):76–83

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Zeng Z, Wang J, Liao X (2005) Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays. IEEE Trans Circ Syst II Express Briefs 52(3):168–173

    Article  Google Scholar 

  6. Song Q (2008) Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach. Neurocomputing 71:2823–2830

    Article  Google Scholar 

  7. Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Networks Learning Syst 23(6):853–865

    Article  Google Scholar 

  8. Song Q, Zhao Z (2016) Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales. Neurocomputing 171:179–184

    Article  Google Scholar 

  9. Lu W, Chen T (2004) Synchronization of coupled connected neural networks with delays. IEEE Trans Circ Syst Part I: Regular Papers 52(12):2491–2503

    Article  MathSciNet  MATH  Google Scholar 

  10. Nie X, Zheng W (2015) Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. Neural Networks 65:65–79

    Article  Google Scholar 

  11. Li T, Luo Q, Sun C, Zhang B (2009) Exponential stability of recurrent neural networks with time-varying discrete and distributed delays. Nonlinear Anal Real World Appl 10:2581–2589

    Article  MathSciNet  MATH  Google Scholar 

  12. Cao J, Yuan K, Ho DW, Lam J (2006) Global point dissipativity of neural networks with mixed time-varying delays. Chaos 16(013105):1–9

    MathSciNet  MATH  Google Scholar 

  13. Lakshmanan S, Senthilkumar T, Balasubramaniam P (2011) Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Appl Math Model 35:5355–5368

    Article  MathSciNet  MATH  Google Scholar 

  14. Samidurai R, Marshal S (2010) Anthon, K. Balachandran. Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal Hybrid Syst 4:103–112

    Article  MathSciNet  MATH  Google Scholar 

  15. Song Q, Zhao Z, Liu Y (2015) Impulsive effects on stability of discrete-time complex-valued neural networks with both discrete and distributed time-varying delays. Neurocomputing 168:1044–1050

    Article  Google Scholar 

  16. Kuang Y (1993) Delay differential equations with applications in population dynamics. Academic Press, Boston

    MATH  Google Scholar 

  17. Brayton R (1966) Bifurcation of periodic solutions in a nonlinear difference-differential equation of neutral type. Quarterly Appl Math 24:215–224

    Article  MathSciNet  MATH  Google Scholar 

  18. Arik S (2014) An analysis of stability of neutral-type neural systems with constant time delays. J Franklin Inst 351:4949–4959

    Article  MathSciNet  MATH  Google Scholar 

  19. Luo Q, Zeng Z, Liao X (2011) Global exponential stability in Lagrange sense for neutral type recurrent neural networks. Neurocomputing 74:638–645

    Article  Google Scholar 

  20. Jian J, Wang B (2015) Stability analysis in Lagrange sense for a class of BAM neural networks of neutral type with multiple time-varying delays. Neurocomputing 149:930–939

    Article  Google Scholar 

  21. Yi Z, Tan K (2004) Convergence analysis of recurrent neural networks. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  22. Liao X, Luo Q, Zeng Z (2008) Positive invariant and global exponential attractive sets of neural networks with time-varying delays. Neurocomputing 71:513–518

    Article  Google Scholar 

  23. Liao X, Luo Q, Zeng Z, Guo Y (2008) Global exponential stability in Lagrange sense for recurrent neural networks with time delays. Nonlinear Anal Real World Appl 9:1535–1557

    Article  MathSciNet  MATH  Google Scholar 

  24. Wu A, Zeng Z (2014) Lagrange stability of memristive neural networks with discrete and distributed delays. IEEE Trans Neural Networks Learning Syst 25(4):690–703

    Article  Google Scholar 

  25. Wu A, Zeng Z (2014) Lagrange stability of neural networks with memristive synapses and multiple delays. Information Sci 280:135–151

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhang G, Shen Y, Xu C (2015) Global exponential stability in a Lagrange sense for memristive recurrent neural networks with time-varying delays. Neurocomputing 149:1330–1336

    Article  Google Scholar 

  27. Li L, Jian J (2015) Exponential convergence and Lagrange stability for impulsive Cohen-Grossberg neural networks with time-varying delays. J Comput Appl Math 277:23–35

    Article  MathSciNet  MATH  Google Scholar 

  28. Tu Z, Cao J, Tasawar H (2016) Global exponential stability in Lagrange sense for inertial neural networks with time-varying delays. Neurocomputing 171:524–531

    Article  Google Scholar 

  29. Boyd S, Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. Society for industrial and applied mathematics, Philadelphia

    Book  MATH  Google Scholar 

  30. Wang X (2015) Uncertainty in learning from big data-editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  Google Scholar 

  31. Lu S, Wang X, Zhang G, Zhou X (2015) Effective algorithms of the Moore-Penrose inverse matrices for extreme learning machine. Intell Data Anal 19(4):743–760

    Article  Google Scholar 

  32. Wang X, Ashfaq R, Fu A (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  33. He Y, Wang X, Huang J (2016) Fuzzy nonlinear regression analysis using a random weight network. Info Sci. doi:10.1016/j.ins.2016.01.037 (in press)

  34. Ashfaq R, Wang X, Huang J, Abbas H, He Y (2016) Fuzziness based semi-supervised learning approach for intrusion detection system (IDS). Information Sci. doi:10.1016/j.ins.2016.04.019 (in press)

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Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China under Grant No. 61174216, the Scientific and Technological Research Program of Chongqing Municipal Education Commission under Grant Nos. KJ1501002 and KJ1401003, and the Youth Fund of Chongqing Three Gorges University under Grant No. 14QN22.

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Authors and Affiliations

  1. Key Laboratory for Nonlinear Science and System Structure, and School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China

    Zhengwen Tu & Liangwei Wang

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  1. Zhengwen Tu
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  2. Liangwei Wang
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Correspondence to Liangwei Wang.

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Tu, Z., Wang, L. Global Lagrange stability for neutral type neural networks with mixed time-varying delays. Int. J. Mach. Learn. & Cyber. 9, 599–609 (2018). https://doi.org/10.1007/s13042-016-0547-6

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  • DOI: https://doi.org/10.1007/s13042-016-0547-6

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