Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper the problem of pullback attractor of neutral Hopfield NNs with mixed time delays and time delay in the leakage term is considered. Based on the Lyapunov–Krasovskii functional method, the theory of pullback attractors and the linear matrix inequalities (LMIs) techniques, some sufficient conditions are established to ensure the existence of the pullback attractor. These conditions are given in terms of LMIs and can be easily numerically checked. Finally, a numerical example is given to appear the effectiveness of our main results.

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

Access this article

Log in via an institution

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

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

References

  1. Ali MS, Saravanakumar R, Cao J (2016) New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays. Neurocomputing 171:1533–1547

    Article  Google Scholar 

  2. Aouiti C (2016) Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays. Cogn Neurodynamics 10(6):573–591

    Article  MathSciNet  Google Scholar 

  3. Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2558-3

    Google Scholar 

  4. Aouiti C, Alimi AM, Karray F, Maalej A (2005) The design of beta basis function neural network and beta fuzzy systems by a hierarchical genetic algorithm. Fuzzy Sets Syst 154(2):251–274

    Article  MathSciNet  MATH  Google Scholar 

  5. Aouiti C, Alimi AM, Maalej A (2002) A genetic-designed beta basis function neural network for multi-variable functions approximation. Syst Anal Model Simul 42(7):975–1009

    Article  MATH  Google Scholar 

  6. Aouiti C, Coirault P, Miaadi F, Moulay E (2017) Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260:378–392

    Article  Google Scholar 

  7. Aouiti C, M’hamdi MS, Cao J, Alsaedi A (2016) Piecewise pseudo almost periodic solution for impulsive generalised high-order Hopfield neural networks with leakage delays. Neural Process Lett 45(2):615–648

    Article  Google Scholar 

  8. Aouiti C, M’hamdi MS, Chérif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46(2):487–506

    Article  Google Scholar 

  9. Aouiti C, M’hamdi MS, Touati A (2017) Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 45(1):121–140

    Article  Google Scholar 

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

    MATH  Google Scholar 

  11. Boyd SP, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA

    Book  MATH  Google Scholar 

  12. Caraballo T, Kloeden PE, Real J (2004) Pullback and forward attractors for a damped wave equation with delays. Stoch Dyn 4(03):405–423

    Article  MathSciNet  MATH  Google Scholar 

  13. Caraballo T, Langa JA, Robinson JC (2001) Attractors for differential equations with variable delays. J Math Anal Appl 260(2):421–438

    Article  MathSciNet  MATH  Google Scholar 

  14. Caraballo T, Łukaszewicz G, Real J (2006) Pullback attractors for asymptotically compact non-autonomous dynamical systems. Nonlinear Anal Theory Methods Appl 64(3):484–498

    Article  MathSciNet  MATH  Google Scholar 

  15. Caraballo T, Marın-Rubio P, Valero J (2005) Autonomous and non-autonomous attractors for differential equations with delays. J Differ Equ 208(1):9–41

    Article  MathSciNet  MATH  Google Scholar 

  16. Cheban D, Schmalfuss B (1999) The global attractors of nonautonomous disperse dynamical systems and differential inclusions. Bull Acad Sci Repub Moldova Math 2:3–22

    MathSciNet  MATH  Google Scholar 

  17. Cheng J, Zhu H, Ding Y, Zhong S, Zhong Q (2014) Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays. Appl Math Comput 242:281–295

    MathSciNet  MATH  Google Scholar 

  18. Crauel H, Debussche A, Flandoli F (1997) Random attractors. J Dyn Differ Equ 9(2):307–341

    Article  MathSciNet  MATH  Google Scholar 

  19. Gao J, Zhu P, Xiong W, Cao J, Zhang L (2016) Asymptotic synchronization for stochastic memristor-based neural networks with noise disturbance. J Frankl Inst 353(13):3271–3289

    Article  MathSciNet  MATH  Google Scholar 

  20. Gong W, Liang J, Cao J (2015) Global \(\mu\)-stability of complex-valued delayed neural networks with leakage delay. Neurocomputing 168:135–144

    Article  Google Scholar 

  21. Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325(2):1117–1132

    Article  MathSciNet  MATH  Google Scholar 

  22. Hale JK (1988) Asymptotic behavior of dissipative systems. Mathematical surveys and monographs. American Mathematical Society, Providence, RI

    Google Scholar 

  23. Hale JK, Lunel SVM (1993) Introduction to functional differential equations. Springer, New York

    Book  MATH  Google Scholar 

  24. Hu VPH, Fan ML, Su P, Chuang CT (2011) Leakage-delay analysis of ultra-thin-body geOI devices and logic circuits. In: 2011 international symposium on VLSI technology, systems and applications (VLSI-TSA). IEEE, pp 1–2

  25. Kloeden PE, Schmalfuss B (1998) Asymptotic behaviour of nonautonomous difference inclusions. Syst Control Lett 33(4):275–280

    Article  MathSciNet  MATH  Google Scholar 

  26. Li T, Fei Sm, Zhu Q (2009) Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal Real World Appl 10(2):1229–1242

    Article  MathSciNet  MATH  Google Scholar 

  27. Li X, Cao J (2017) An impulsive delay inequality involving unbounded time-varying delay and applications. IEEE Trans Autom Control 62(7):3618–3625

    Article  MathSciNet  MATH  Google Scholar 

  28. Li X, Song S (2013) Impulsive control for existence, uniqueness, and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans Neural Netw Learn Syst 24(6):868–877

    Article  Google Scholar 

  29. Li X, Song S (2017) Stabilization of delay systems: delay-dependent impulsive control. IEEE Trans Autom Control 62(1):406–411

    Article  MathSciNet  MATH  Google Scholar 

  30. Li X, Wu J (2016) Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica 64:63–69

    Article  MathSciNet  MATH  Google Scholar 

  31. Li Y, Zeng Z, Wen S (2016) Asymptotic stability analysis on nonlinear systems with leakage delay. J Frankl Inst 353(3):757–779

    Article  MathSciNet  MATH  Google Scholar 

  32. Lofberg J (2004) Yalmip: a toolbox for modeling and optimization in matlab. In: 2004 IEEE international symposium on computer aided control systems design, pp 284–289

  33. M’Hamdi MS, Aouiti C, Touati A, Alimi AM, Snasel V (2016) Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci 36(6):1662–1682

    Article  MathSciNet  MATH  Google Scholar 

  34. Michel AN, Farrell JA, Porod W (1989) Qualitative analysis of neural networks. IEEE Trans Circuits Syst 36(2):229–243

    Article  MathSciNet  MATH  Google Scholar 

  35. Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal Real World Appl 11(3):2141–2151

    Article  MathSciNet  MATH  Google Scholar 

  36. Peng W, Wu Q, Zhang Z (2016) LMI-based global exponential stability of equilibrium point for neutral delayed BAM neural networks with delays in leakage terms via new inequality technique. Neurocomputing 199:103–113

    Article  Google Scholar 

  37. Plemmons R, Berman A (1979) Nonnegative matrices in the mathematical sciences. Chap 6:137

  38. Rajavel S, Samidurai R, Cao J, Alsaedi A, Ahmad B (2017) Finite-time non fragile passivity control for neural networks with time varying delay. Appl Math Comput 297:145–158

    MathSciNet  MATH  Google Scholar 

  39. Velmurugan G, Rakkiyappan R, Vembarasan V, Cao J, Alsaedi A (2016) Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay. Neural Netw 86:42–53

    Article  Google Scholar 

  40. Wan L, Zhou Q, Liu J (2017) Delay-dependent attractor analysis of Hopfield neural networks with time-varying delays. Chaos Solitons Fractals 101:68–72

    Article  MathSciNet  MATH  Google Scholar 

  41. Wang Z, Liu Y, Liu X (2005) On global asymptotic stability of neural networks with discrete and distributed delays. Phys Lett A 345(4):299–308

    Article  MATH  Google Scholar 

  42. Wang Z, Wei G, Feng G (2009) Reliable \({H}_\infty\) control for discrete-time piecewise linear systems with infinite distributed delays. Automatica 45(12):2991–2994

    Article  MathSciNet  MATH  Google Scholar 

  43. Wu Y, Cao J, Alofi A, Abdullah AM, Elaiw A (2015) Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay. Neural Netw 69:135–143

    Article  MATH  Google Scholar 

  44. Yan Z, Zhang W, Zhang G (2015) Finite-time stability and stabilization of itô stochastic systems with Markovian switching: mode-dependent parameter approach. IEEE Trans Autom Control 60(9):2428–2433

    Article  MATH  Google Scholar 

  45. Zhang H, Wang Z, Liu D (2014) A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(7):1229–1262

    Article  Google Scholar 

  46. Zheng C, Li N, Cao J (2015) Matrix measure based stability criteria for high-order neural networks with proportional delay. Neurocomputing 149:1149–1154

    Article  Google Scholar 

  47. Zhou Q, Wan L (2015) Pullback attractor for Hopfield neural networks. Pac J Appl Math 7(2):133–141

    MathSciNet  MATH  Google Scholar 

  48. Zhou Q, Wan L, Fu H, Zhang Q (2016) Pullback attractor for Cohen–Grossberg neural networks with time-varying delays. Neurocomputing 171:510–514

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Units of Mathematics and Applications UR13ES47, Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, 7021, Zarzouna, Bizerta, Tunisia

    Chaouki Aouiti & Foued Miaadi

Authors
  1. Chaouki Aouiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Foued Miaadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaouki Aouiti.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., Miaadi, F. Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays. Neural Comput & Applic 31, 4113–4122 (2019). https://doi.org/10.1007/s00521-017-3314-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3314-z

Keywords

Search

Navigation