Skip to main content
SpringerLink
Log in

Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper is concerned with the problems of existence and stability of the periodic solution for a class of neutral-type neural networks. The neural network addressed is general where the time delays and difference operator are taken into account. By employing the Mawhin’s continuation theorem, the sufficient condition is obtained to guarantee the existence and uniqueness of the periodic solution for the neutral-type neural networks. By constructing a novel Lyapunov functional, a unified framework is established to derive sufficient conditions for the concerned system to be globally exponentially stable. A numerical example is provided to demonstrate the usefulness of the main results obtained.

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. 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 

  2. Liu Y, Liu W, Obaid MA, Abbas IA (2016) Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays. Neurocomputing 177:409–415

    Article  Google Scholar 

  3. Li L, Ho DWC, Lu J (2013) A unified approach to practical consensus with quantized data and time delay. IEEE Trans Circuits Syst I 60(10):2668–2678

    Article  MathSciNet  Google Scholar 

  4. Li L, Ho DWC, Cao J, Lu J (2016) Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism. Neural Netw 76:1–12

    Article  Google Scholar 

  5. Lu J, Ho DWC (2011) Stabilization of complex dynamical networks with noise disturbance under performance constraint. Nonlinear Anal Ser B 12:1974–1984

    Article  MathSciNet  MATH  Google Scholar 

  6. Lu J, Wang Z, Cao J, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176

    Article  MATH  Google Scholar 

  7. Kao Y, Shi L, Xie J, Karimi HR (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30

    Article  MATH  Google Scholar 

  8. Zhao H, Wang K (2006) Dynamical behaviors of Cohen-Grossberg neural networks with delays and reaction-diffusion terms. Neurocomputing 70:536–543

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Arik S (2014) An improved robust stability result for uncertain neural networks with multiple time delays. Neural Netw 54:1–10

    Article  MATH  Google Scholar 

  11. Baldi P, Atiya AF (1994) How delays affect neural dynamics and learning. IEEE Trans Neural Netw 5:612–621

    Article  Google Scholar 

  12. Zhu Q, Cao J (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 21:1314–1325

    Article  Google Scholar 

  13. Song Q, Cao J (2010) On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans Circuits Syst I 57:672–680

    Article  MathSciNet  Google Scholar 

  14. Song Q, Cao J (2007) Impulsive effects on stability of fuzzy Cohen–Grossberg neural networks with time-varying delays. IEEE Trans Syst Man Cybern B 37:733–741

    Article  Google Scholar 

  15. Yang F, Wang Z, Hung YS (2002) Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noise. IEEE Trans Autom Control 47:1179–1183

    Article  MathSciNet  Google Scholar 

  16. Zhai G, Xu X, Ho DWC (2012) Stability of switched linear discrete-time descriptor systems: a new commutation condition. Int J Control 85:1779–1788

    Article  MathSciNet  MATH  Google Scholar 

  17. Dong H, Wang Z, Ho DWC, Gao H (2010) Robust H-infinity fuzzy output-feedback control with multiple probabilistic delays and multiple missing measurements. IEEE Trans Fuzzy Syst 18:712–725

    Article  Google Scholar 

  18. Lu J, Wang Z, Cao J, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int J Bifurc Chaos 22:1250176

    Article  MATH  Google Scholar 

  19. 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 

  20. Xu S, Lam J, Ho D, Zou Y (2005) Delay-dependent exponential stability for a class of neural networks with time delays. J Comput Appl Math 183:16–28

    Article  MathSciNet  MATH  Google Scholar 

  21. Lien C, Yu K, Lin Y, Chung Y, Chung L (2009) Exponential convergence rate estimation for uncertain delayed neural networks of neutral type. Chao Solit Fract 40:2491–2499

    Article  MathSciNet  MATH  Google Scholar 

  22. 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 

  23. Li X (2009) Global exponential stability for a class of neural networks. Appl Math Lett 22:1235–1239

    Article  MathSciNet  MATH  Google Scholar 

  24. Rakkiyappan R, Balasubramaniam P, Cao J (2010) Global exponential stability results for neutral-type impulsive neural networks. Nonlinear Anal Real 11:122–130

    Article  MathSciNet  MATH  Google Scholar 

  25. 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 

  26. Hale J (1977) Theory of functional differential equations. Applied mathematical science, vol 3. Springer, NewYork

    Book  Google Scholar 

  27. Du B, Guo L, Ge W, Lu S (2009) Periodic solutions for generalized Liénard neutral equation with variable parameter. Nonlinear Anal 70:2387–2394

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  30. Bai C, Du B (2013) Periodic Solutions for a kind of neutral Rayleigh equations with variable parameter. Results Math 63:567–580

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  32. Zhang A, Qiu J, She J (2014) Existence and global exponential stability of periodic solution for high-order discrete-time BAM neural networks. Neural Netw 50:98–109

    Article  MATH  Google Scholar 

  33. Li T, Zheng W, Lin C (2011) Delay-slope dependent stability results of recurrent neural networks. IEEE Trans Neural Netw 22:2138–2143

    Article  Google Scholar 

  34. Wang Z, Wang Y, Liu Y (2010) Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans Neural Netw 21:11–25

    Article  Google Scholar 

  35. Han Q-L, Liu Y, Yang F (2016) Optimal communication network-based H-infinity quantized control with packet dropouts for a class of discrete-time neural networks with distributed time delay. IEEE Trans Neural Netw Learn Syst 27(2):426–434

    Article  Google Scholar 

  36. Liu Y, Wang Y, Zhu X, Liu X (2014) Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays. Int J Syst Sci 45(7):1528–1538

    Article  MathSciNet  MATH  Google Scholar 

  37. Liu Y, Alsaadi F, Yin X, Wang Y (2015) Robust H-infinity filtering for discrete nonlinear delayed stochastic systems with missing measurements and randomly occurring nonlinearities. Int J Gen Syst 44(2):169–181

    Article  MathSciNet  MATH  Google Scholar 

  38. Hou N, Dong H, Wang Z, Ren W, Alsaadi FE (2016) Non-fragile state estimation for discrete Markovian jumping neural networks. Neurocomputing 179(29):238–245

    Article  Google Scholar 

  39. Yu Y, Dong H, Wang Z, Ren W, Alsaadi FE (2016) Design of non-fragile state estimators for discrete time-delayed neural networks with parameter uncertainties. Neurocomputing 182(19):18–24

    Article  Google Scholar 

  40. Dong H, Wang Z, Alsaadi FE, Ahmad B (2015) Event-triggered robust distributed state estimation for sensor networks with state-dependent noises. Int J Gen Syst 44(2):254–266

    Article  MathSciNet  MATH  Google Scholar 

  41. Dong H, Wang Z, Ding S, Gao H (2015) Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization. Automatica 52:355–362

    Article  MathSciNet  MATH  Google Scholar 

  42. Shen J, Tan H, Wang J, Wang J, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178

    Google Scholar 

  43. Xie S, Wang Y (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel Pers Commun 78(1):231–246

    Article  Google Scholar 

  44. Ma T et al (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inf Syst E98–D(4):902–910

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61374010, 61074129, 11671008, and 61175111, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012682, and the Six Talents Peak Project of Jiangsu Province (2012).

Author information

Authors and Affiliations

  1. Department of Mathematics, Yangzhou University, Yangzhou, 225002, China

    Yurong Liu & Bo Du

  2. Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu, 223300, People’s Republic of China

    Bo Du

  3. Department of Electrical and Computer Eninering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Yurong Liu

  4. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Ahmed Alsaedi

Authors
  1. Yurong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yurong Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Du, B. & Alsaedi, A. Existence and Global Exponential Stability of Periodic Solution for a Class of Neutral-Type Neural Networks with Time Delays. Neural Process Lett 45, 981–993 (2017). https://doi.org/10.1007/s11063-016-9549-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-016-9549-3

Keywords

Search

Navigation