Skip to main content

Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach

The European Physical Journal B volume 88, Article number: 109 (2015) Cite this article

Abstract

In this paper, exponential anti-synchronization in mean square of an uncertain memristor-based neural network is studied. The uncertain terms include non-modeled dynamics with boundary and stochastic perturbations. Based on the differential inclusions theory, linear matrix inequalities, Gronwall’s inequality and adaptive control technique, an adaptive controller with update laws is developed to realize the exponential anti-synchronization. Adaptive controller can adjust itself behavior to get the best performance, according to the environment is changing or the environment has changed, which has the ability to adapt to environmental change. Furthermore, a numerical example is provided to validate the effectiveness of the proposed method.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. J. Borghetti, G.S. Snider, P.J. Kuekes Yang, J. Yang, D.R. Stewart, R. Stanley Williams, Nature 464, 873 (2010)

    Article  ADS  Google Scholar 

  2. Y.V. Pershin, M. Di Ventra, Neural Netw. 23, 881 (2010)

    Article  Google Scholar 

  3. S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nano Lett. 10, 1297 (2010)

    Article  ADS  Google Scholar 

  4. A. Thomas, J. Phys. D 46, 1 (2013)

    MATH  Google Scholar 

  5. B.S. Dmitri, R.S. Duncan, R.S. Williams, Nature 453, 80 (2008)

    Article  Google Scholar 

  6. Y.V. Pershin, S.L. Fontaine, M. Di Ventra, Phys. Rev. E 80, 021926 (2009)

    Article  ADS  Google Scholar 

  7. L.O. Chua, L. Yang, IEEE Trans. Circuits Syst. 35, 1257 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. S.P. Wen, Z.G. Zeng, T.W. Huang, Neural Comput. Appl. 23, 815 (2013)

    Article  Google Scholar 

  9. A.L. Wu, J. Zhang, Z.G. Zeng, Phys. Lett. A 375, 1661 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. S.P. Wen, Z.G. Zeng, T.W. Huang, Neurocomputing 97, 233 (2012)

    Article  Google Scholar 

  11. G. Wang, Y. Shen, Neural Comput. Appl. 24, 1421 (2014)

    Article  Google Scholar 

  12. Z.Y. Guo, J. Wang, Z. Yan, Neural Netw. 48, 158 (2013)

    Article  MATH  Google Scholar 

  13. G.D. Zhang, Y. Shen, Neural Netw. 55, 1 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  14. H.Q. Wu, L.Y. Zhang, S.B. Ding, X.Q. Guo, L.L. Wang, Discrete Dyn. Nat. Soc. 2013, 140153 (2013)

    MathSciNet  Google Scholar 

  15. A.L. Wu, Z.G. Zeng, Commun. Nonlinear Sci. Numer. Simul. 18, 373 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. G.D. Zhang, Y. Shen, L.M. Wang, Neural Netw. 46, 1 (2013)

    Article  MATH  Google Scholar 

  17. C.Q. Guo, Y. Gao, Inform. Technol. J. 13, 2356 (2014)

    Article  MathSciNet  Google Scholar 

  18. W.P. Wang, L.X. Li, H.P. Peng, J.H. Xiao, Y.X. Yang, Nonlin. Dyn. 76, 591 (2014)

    Article  MathSciNet  Google Scholar 

  19. H. Zhao, L.L. Li, H.P. Peng, J.H. Xiao, Y.X. Yang, Eur. Phys. J. B 88, 45 (2015)

    ADS  MathSciNet  Google Scholar 

  20. L.X. Li, J. Kurths, H.P. Peng, Y.X. Yang, Q. Luo, Eur. Phys. J. B 86, 125 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  21. T.B. Wang, W.N. Zhou, S.W. Zhao, Commun. Nonlinear Sci. Numer. Simul. 18, 2097 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. Y. Fang, K. Yan, K.L. Li, Math. Problems Eng. 2014, 963081 (2014)

    MathSciNet  Google Scholar 

  23. W.P. Wang, L.X. Li, H.P. Peng, J.H. Xiao, Y.X. Yang, Neural Netw. 53, 8 (2014)

    Article  MATH  Google Scholar 

  24. Z.G. Zeng, J. Wang, X.X. Liao, IEEE Trans. Circuits Syst. I 50, 1353 (2003)

    Article  MathSciNet  Google Scholar 

  25. C.K. Ahn, Inform. Sci. 180, 4582 (2010)

    Article  MATH  Google Scholar 

  26. M. Itoh, L.O. Chua, Int. J. Bifurc. Chaos 19, 3605 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. J. Aubin, H. Frankowska, Set-Valued Analysis (Birkhäuser, Boston, 1990)

  28. A. Filippov, Mathematics and its applications (Kluwer Academic, Boston, 1984)

  29. B. Øksendal, Stochastic differential equations – an introduction with applications (Springer, New York, 2005)

  30. Y.Y. Wang, L.H. Xie, C.E. de Souza, Syst. Control Lett. 19, 139 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China

    Hui Zhao & Jinghua Xiao

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China

    Lixiang Li, Haipeng Peng & Yixian Yang

  3. Potsdam Institute for Climate Impact Research, 14473, Potsdam, Germany

    Jürgen Kurths

Authors
  1. Hui Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lixiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haipeng Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jürgen Kurths
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jinghua Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yixian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lixiang Li.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, H., Li, L., Peng, H. et al. Anti-synchronization for stochastic memristor-based neural networks with non-modeled dynamics via adaptive control approach. Eur. Phys. J. B 88, 109 (2015). https://doi.org/10.1140/epjb/e2015-50798-9

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-50798-9

Keywords

  • Statistical and Nonlinear Physics