Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Periodic Solution for Neutral-Type Neural Networks in Critical Case

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

A generalized neutral-type neural networks in critical case is studied. Some existence and asymptotic behavior results of periodic solution to the neutral-type neural networks in critical case are obtained by continuation theorem of coincidence degree theory and some analysis techniques. Finally, an example is given to show the effectiveness of the results in this paper.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Samli R, Arik S (2009) New results for global stability of a class of neutral-type neural systems with time delays. Appl Math Comput 210:564–570

    MathSciNet  MATH  Google Scholar 

  2. Wang K, Zhu Y (2010) Stability of almost periodic solution for a generalized neutral-type neural networks with delays. Neurocomputing 73:3300–3307

    Article  Google Scholar 

  3. Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364:267–273

    Article  MATH  Google Scholar 

  4. Rakkiyappan R, Balasubramaniama P, Caob J (2010) Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal 11:122–130

    Article  MathSciNet  Google Scholar 

  5. Liu Y, Wang Z, Liu X (2012) Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays. Neurocomputing 94:46–53

    Article  Google Scholar 

  6. Serra E (1991) Periodic solutions for some nonlinear differential equations of neutral type. Nonlinear Anal 17:139–151

    Article  MathSciNet  MATH  Google Scholar 

  7. Lu S, Ge W (2003) On the existence of periodic solutions for neutral functional differential equation. Nonlinear Anal. 54:1285–1306

    Article  MathSciNet  MATH  Google Scholar 

  8. Lu S, Ren J, Ge W (2003) The problems of periodic solutions for a kind of second order neutral functional differential equation. Appl Anal 82:411–426

    Article  MathSciNet  MATH  Google Scholar 

  9. Agarwal R, Grace S (2000) Asymptotic stability of certain neutral differential equations. Math Comput Model 31:9–15

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang Y, Xu S, Chu Y, Lu J (2010) Robust global synchronization of complex networks with neutral-type delayed nodes. Appl Math Comput 216:768–778

    MathSciNet  MATH  Google Scholar 

  11. Du B (2013) Periodic solutions to \(p\)-laplacian neutral lienard type equation with variable parameter. Math Slovaca 2:1–15

    Google Scholar 

  12. Du B, Sun B (2011) Periodic solutions to a \(p-\)Laplacian neutral Duffing equation with variable parameter. Electron J Qual Theory Differ Equ 55:1–18

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu S, Ge W (2004) Periodic solutions to a kind of neutral functional differential equation in the critical case. J Math Anal Appl 293:462–475

    Article  MathSciNet  MATH  Google Scholar 

  14. Gaines R, Mawhin J (1977) Coincidence degree and nonlinear differential equations. Springer, Berlin

    Book  MATH  Google Scholar 

  15. Barbalat I (1959) Systems d’equations differential d’oscillationsn onlinearities. Rev Rounmaine Math Pure Appl 4:267–270

    MathSciNet  Google Scholar 

  16. Agarwal RP, Grace SR (2000) Asymptotic stability of differential systems of neutral type. Appl Math Lett 13:15–19

    Article  MathSciNet  MATH  Google Scholar 

  17. Rakkiyappan R, Balasubramaniam P (2008) New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71:1039–1045

    Article  MATH  Google Scholar 

  18. Cheng C, Liao T, Yan J, Hwang C (2006) Globally asymptotic stability of a class of neutral-type neural networks with delays. IEEE Trans Syst, Man, Cybern B, Cybern 36:1191–1195

    Article  Google Scholar 

  19. Cheng L, Hou Z, Tan M (2008) A neutral-type delayed projection neural network for solving nonlinear variational inequalities. IEEE Trans Circuits Syst II, Exp Briefs 55:806–810

    Article  Google Scholar 

  20. Zhang H, Liu Z, Huang GB (2010) Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE Trans Syst Man Cybern B Cybern 40:1480–1490

    Article  Google Scholar 

  21. Liu Y, Wang Z, Liang J, Liu X (2013) Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays. IEEE Trans Syst Man Cybern B Cybern 43:102–114

    Google Scholar 

Download references

Acknowledgments

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, under Grant No. 9-130-36-HiCi, NNSF (No. 11571136) of China and Postdoctoral Foundation of China (2014M561716). The authors, therefore, acknowledge with thanks DSR technical and financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bo Du.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, B., Lu, S. & Liu, Y. Periodic Solution for Neutral-Type Neural Networks in Critical Case. Neural Process Lett 44, 765–777 (2016). https://doi.org/10.1007/s11063-015-9493-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-015-9493-7

Keywords

Navigation