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Stability of Hopfield neural networks with time delays and variable-time impulses

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Abstract

The stability of Hopfield neural networks with fixed-time impulses has been intensively investigated in recent years. However, few existing publications addressed the stability of delayed neural networks with variable-time impulses. In this paper, we consider the case of variable-time impulses and attempt to establish the general stability criteria. It shows that the proposed results can also be applied to the case of fixed-time impulses, which provide a new stability condition for the case of fixed-time impulses. To illustrate the effectiveness of our theoretical results, numerical examples and simulations are also presented.

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References

  1. Akca H, Alassar R, Covachev V, Covacheva Z, Al-Zahrani E (2004) Continuous-time additive Hopfield-type neural network with impulses. J Math Anal Appl 290:436–451

    Article  MathSciNet  MATH  Google Scholar 

  2. Berman A, Plemmons RJ (1979) Nonnegative matrices in mathematical sciences. Academic Press, New York

    MATH  Google Scholar 

  3. Chen T (2001) Global exponential stability of delayed Hopfield neural networks. Neural Netw 14:977–980

    Article  Google Scholar 

  4. Fu XL, Qi JG, Liu YS (2000) General comparison principle for impulsive variable time differential equations with application. Nonlinear Anal 42:1421–1429

    Article  MathSciNet  MATH  Google Scholar 

  5. Gopalsamy K, He XZ (1994) Stability in asymmetric Hopfield nets with transmission delays. Physica D 76:344–358

    Article  MathSciNet  MATH  Google Scholar 

  6. Guan ZH, Chen G (1999) On delayed impulsive Hopfield neural networks. Neural Netw 12:273–280

    Article  Google Scholar 

  7. Guan ZH, Chen GR, Qin Y (2000) On equilibria, stability, and instability of Hopfield neural networks. IEEE Trans Neural Netw 11:534–540

    Article  Google Scholar 

  8. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA Biophys 81:3088–3092

    Article  Google Scholar 

  9. Huang ZT, Yang QG, Luo XS (2008) Exponential stability of impulsive neural networks with time-varying delays. Chaos Solitons Fractals 35:770–780

    Article  MATH  Google Scholar 

  10. Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10:1366–1374

    Article  Google Scholar 

  11. Kaul SK (1997) Vector lyapunov functions in impulsive variable-time differential systems. Nonlinear Anal Theory Methods Appl 30:2695–2698

    Article  MathSciNet  MATH  Google Scholar 

  12. Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulsive differential equations. World Scientific, Singapore

    Book  MATH  Google Scholar 

  13. Lakshmikantham V, Leela S, Kaul S (1994) Comparison principle for impulsive differential equations with variable times and stability theory. Nonlinear Anal 22:499–503

    Article  MathSciNet  MATH  Google Scholar 

  14. Lee DL (1999) New stability conditions for Hopfield networks in partial simultaneous update mode. IEEE Trans Neural Netw 10:975–978

    Article  Google Scholar 

  15. Li CD, Li CJ, Liu C (2009) Destabilizing effects of impulsive in delayed BAM neural networks. Modern Phys Lett B 23:3503–3513

    Article  MATH  Google Scholar 

  16. Li CJ, Li CD, Liao XF et al (2011) Impulsive effects on stability of high-order BAM neural networks with time-delays. Neurocomputing 74:1541–1550

    Article  Google Scholar 

  17. Liang XB (2000) Equivalence between local exponential stability of the unique equilibrium point and global stability for Hopfield-type neural networks with two neurons. IEEE Trans Neural Netw 11:1194–1196

    Article  Google Scholar 

  18. Liu X, Ballinger G (2002) Existence and continuability of solutions for differential equations with delays and state-dependent impulses. Nonlinear Anal 51:633–647

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu C, Li CD, Liao XF (2011) Variable-time impulses in BAM neural networks with delays. Neurocomputing. doi:10.1016/j.neucom.2011.05.005

  20. Long SJ, Xu DY (2008) Delay-dependent stability analysis for impulsive neural networks with time varying delays. Neurocomputing 71:1705–1713

    Article  Google Scholar 

  21. Van Den Driessche P, Zou XF (1998) Global attractivity in delayed Hopfield neural networks models. SIAM J Appl Math 58:1878–1890

    Article  MathSciNet  MATH  Google Scholar 

  22. Xu D, Zhao H, Zhu H (2001) Global dynamics of Hopfield neural networks involving variable delays. Comput Math Appl 42:39–45

    Article  MathSciNet  MATH  Google Scholar 

  23. Yang T (2001) Impulsive control theory. Springer, Berlin

    MATH  Google Scholar 

  24. Yang XF (2005) Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distribute delays. Phys Lett A 343:108–116

    Article  MATH  Google Scholar 

  25. Yang H, Dillon TS (1994) Exponential stability and oscillation of Hopfield graded response neural network. IEEE Trans Neural Netw 5:719–729

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the associate editor and reviewers for their constructive comments based on which the presentation of the paper has been greatly improved. The work described in this paper was partially supported by the Fundamental Research Funds for the Central Universities of China (Project No. CDJZR10 18 55 01) and National Natural Science Foundation of China (Grant No.60974020).

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Authors and Affiliations

  1. College of Computer, Chongqing University, Chongqing, 400044, People’s Republic of China

    Chao Liu, Chuandong Li & Chaojie Li

  2. Texas A&M University at Qatar, Doha, P.O. Box 23874, Qatar

    Tingwen Huang

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  1. Chao Liu
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  2. Chuandong Li
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  3. Tingwen Huang
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  4. Chaojie Li
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Correspondence to Chuandong Li.

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Liu, C., Li, C., Huang, T. et al. Stability of Hopfield neural networks with time delays and variable-time impulses. Neural Comput & Applic 22, 195–202 (2013). https://doi.org/10.1007/s00521-011-0695-2

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  • DOI: https://doi.org/10.1007/s00521-011-0695-2

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