Skip to main content
SpringerLink
Log in

Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In this paper, we study the finite-time stability and synchronization problem of a class of memristor-based fractional-order Cohen-Grossberg neural network (MFCGNN) with the fractional order α ∈ (0,1 ]. We utilize the set-valued map and Filippov differential inclusion to treat MFCGNN because it has discontinuous right-hand sides. By using the definition of Caputo fractional-order derivative, the definitions of finite-time stability and synchronization, Gronwall’s inequality and linear feedback controller, two new sufficient conditions are derived to ensure the finite-time stability of our proposed MFCGNN and achieve the finite-time synchronization of drive-response systems which are constituted by MFCGNNs. Finally, two numerical simulations are presented to verify the rightness of our proposed theorems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Cohen, S. Grossberg, IEEE Trans. Syst. Man Cybernet. 13, 815 (1983)

    Article  MathSciNet  Google Scholar 

  2. Q. Zhu, X. Li, Fuzzy Sets Syst. 203, 74 (2012)

    Article  Google Scholar 

  3. X. Yang, J. Cao, W. Yu, Cogn. Neurodyn. 8, 239 (2014)

    Article  Google Scholar 

  4. Q. Zhu, J. Cao, R. Rakkiyappan, Nonlinear Dynamics 79, 1085 (2015)

    Article  MathSciNet  Google Scholar 

  5. X. Nie, W.X. Zheng, J. Cao, Neural Networks 71, 27 (2015)

    Article  Google Scholar 

  6. K. Sun, A. Zhang, J. Qiu, X. Chen, C. Yang, X. Chen, Neural Networks 61, 68 (2015)

    Article  Google Scholar 

  7. M. Şaylı, E. Yılmaz, Neurocomputing 171, 1375 (2016)

    Article  Google Scholar 

  8. K. Oldham, J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order (Academic Press, New York-London, 1974)

  9. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (John Wiley & Sons, New York, 1993)

  10. I. Podlubny, in Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Academic Press, 1998), Vol. 198

  11. C.F. Lorenzo, T.T. Hartley, Nonlinear Dynamics 29, 57 (2002)

    Article  MathSciNet  Google Scholar 

  12. R. Bárcena, M. De la Sen, IEE Proc.-Control Theory Appl. 150, 183 (2003)

  13. M.D. Ortigueira, C.J. Matos, M.S. Piedade, Nonlinear Dynamics 29, 173 (2002)

    Article  MathSciNet  Google Scholar 

  14. I. Podlubny, I. Petraš, B.M. Vinagre, P. O’leary, L. Dorčák, Nonlinear Dynamics 29, 281 (2002)

    Article  MathSciNet  Google Scholar 

  15. J.G. Lu, Phys. Lett. A 354, 305 (2006)

    Article  ADS  Google Scholar 

  16. L. Chen, J. Qu, Y. Chai, R. Wu, G. Qi, Entropy 15, 3265 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  17. H.J. Kwon, K. Sengupta, V.M. Yakovenko, Eur. Phys. J. B 37, 349 (2004)

    Article  ADS  Google Scholar 

  18. A.A. Stanislavsky, Eur. Phys. J. B 49, 93 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  19. B.N. Lundstrom, M.H. Higgs, W.J. Spain, A.L. Fairhall, Nat. Neurosci. 11, 1335 (2008)

    Article  Google Scholar 

  20. L.O. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)

    Article  Google Scholar 

  21. D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)

    Article  ADS  Google Scholar 

  22. I. Stamova, Nonlinear Dynamics 77, 1251 (2014)

    Article  MathSciNet  Google Scholar 

  23. H. Bao, J.H. Park, J. Cao, Nonlinear Dynamics 82, 1343 (2015)

    Article  MathSciNet  Google Scholar 

  24. H. Zhao, L. Li, H. Peng, J. Kurths, J. Xiao, Y. Yang, Eur. Phys. J. B 88, 1 (2015)

    MathSciNet  Google Scholar 

  25. Z. Ding, Y. Shen, L. Wang, Neural Networks 73, 77 (2016)

    Article  Google Scholar 

  26. D.L. Debeljković, M.P. Lazarević, D. Koruga, S. Milinković, M. Jovanović, L.A. Jacić, Facta Universitatis-Series: Mechanics, Automatic Control and Robotics 3, 231 (2001)

    MathSciNet  Google Scholar 

  27. M.P. Lazarević, A.M. Spasić, Math. Comput. Modell. 49, 475 (2009)

    Article  Google Scholar 

  28. X. Chen, L. Huang, Z. Guo, Neurocomputing 103, 43 (2013)

    Article  Google Scholar 

  29. G. Velmurugan, R. Rakkiyappan, J. Cao, Neural Networks 73, 36 (2016)

    Article  Google Scholar 

  30. H. Kim, M.P. Sah, C. Yang, T. Roska, L.O. Chua, Proc. IEEE 100, 2061 (2012)

    Article  Google Scholar 

  31. A. Wu, Z. Zeng, Neural Networks 36, 1 (2012)

    Article  Google Scholar 

  32. G. Zhang, Y. Shen, Neural Networks 55, 1 (2014)

    Article  MathSciNet  Google Scholar 

  33. A.F. Filippov, Matematicheskii sbornik 93, 99 (1960)

    Google Scholar 

  34. J.P. Aubin, A. Cellina, Differential inclusions: set-valued maps and viability theory (Springer-Verlag, New York, Inc., 1984)

  35. A.F. Filippov, F.M. Arscott, in Differential equations with discontinuous righthand sides: control systems (Springer Science Business Media, 1988), Vol. 18

  36. H. Ye, J. Gao, Y. Ding, J. Math. Anal. Appl. 328, 1075 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Mingwen Zheng, Jinghua Xiao & Hui Zhao

  2. School of Science, Shandong University of Technology, Zibo, 255000, P.R. China

    Mingwen Zheng

  3. Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China

    Lixiang Li, Haipeng Peng & Yixian Yang

Authors
  1. Mingwen Zheng
    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. Jinghua Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yixian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hui Zhao
    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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, M., Li, L., Peng, H. et al. Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network. Eur. Phys. J. B 89, 204 (2016). https://doi.org/10.1140/epjb/e2016-70337-6

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70337-6

Keywords

Search

Navigation