Skip to main content
Log in

Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper is concerned with a class of neutral type recurrent neural networks with time-varying delays, distributed delay and D operator on time–space scales which unify the continuous-time and the discrete-time recurrent neural networks under the same framework. Some sufficient conditions are given for the existence and the global exponential stability of the pseudo almost periodic solution by using inequality analysis techniques on time scales, fixed point theorem and the theory of calculus on time scales. An example is given to show the effectiveness of the derived results via computer simulations.

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

Access this article

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

References

  1. Wen S, Hu R, Yang Y, Huang T, Zeng Z, Song YD (2018) Memristor-based echo state network with online least mean square. IEEE Trans Syst Man Cybern Syst 99:1–10

    Google Scholar 

  2. Wen S, Xiao S, Yan Z, Zeng Z, Huang T (2018) Adjusting learning rate of memristor-based multilayer neural networks via fuzzy method. IEEE Trans Comput Aided Des Integr Circuits Syst. https://doi.org/10.1109/TCAD.2018.2834436

  3. Wen S, Liu W, Yang Y, Huang T, Zeng Z (2018) Generating realistic videos from keyframes with concatenated GANs. IEEE Trans Circuits Syst Video Technol. https://doi.org/10.1109/TCSVT.2018.2867934

    Google Scholar 

  4. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554–2558

    Article  MathSciNet  MATH  Google Scholar 

  5. Aouiti C, Gharbia IB, Cao J, Alsaedi A (2019) Dynamics of impulsive neutral-type BAM neural networks. J Frankl Inst. https://doi.org/10.1016/j.jfranklin.2019.01.028

    MathSciNet  MATH  Google Scholar 

  6. Aouiti C, Gharbia IB, Cao J, M’hamdi MS, Alsaedi A (2018) Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms. Chaos Solitons Fractals 107:111–127

    Article  MathSciNet  MATH  Google Scholar 

  7. Alimi AM, Aouiti C, Assali EA (2019) Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication. Neurocomputing 332:29–43

    Article  Google Scholar 

  8. Cao J, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I Regul Pap 52(2):417–426

    Article  MathSciNet  MATH  Google Scholar 

  9. Cao J, Wang L (2002) Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans Neural Netw 13(2):457–463

    Article  Google Scholar 

  10. Aouiti C, Miaadi F (2018) Finite-time stabilization of neutral Hopfield neural networks with mixed delays. Neural Process Lett. 48:1645–1669. https://doi.org/10.1007/s11063-018-9791-y

    Article  Google Scholar 

  11. Alimi AM, Aouiti C, Chérif F, Dridi F, M’hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing 321:274–295. https://doi.org/10.1016/j.neucom.2018.01.061

    Article  Google Scholar 

  12. Aouiti C, Miaadi F (2018) Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3314-z

  13. 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 

  14. Li X, Song S, Wu J (2018) Impulsive control of unstable neural networks with unbounded time-varying delays. Sci China Inf Sci 61(1):012203

    Article  Google Scholar 

  15. Xiao Q, Huang T, Zeng Z (2018) Global exponential stability and synchronization for discrete-time inertial neural networks with time delays: a timescale approach. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2018.2874982

    Google Scholar 

  16. Cao J, Huang DS, Qu Y (2005) Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 23(1):221–229

    Article  MathSciNet  MATH  Google Scholar 

  17. 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 

  18. Huang Q, Cao J (2017) Stability analysis of inertial Cohen–Grossberg neural networks with Markovian jumping parameters. Neurocomputing. https://doi.org/10.1016/j.neucom.2017.12.028

    Google Scholar 

  19. 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 

  20. Chen Z (2017) Global exponential stability of anti-periodic solutions for neutral type CNNs with \(D\) operator. Int J Mach Learn Cybern 9:1109–1115. https://doi.org/10.1007/s13042-016-0633-9

    Article  Google Scholar 

  21. Liu B (2016) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Methods Appl Sci 40:167–174. https://doi.org/10.1002/mma.3976

    Article  MathSciNet  MATH  Google Scholar 

  22. Aouiti C (2016) Oscillation of impulsive neutral delay generalized high-order Hopfield neural networks. Neural Comput Appl 29:477–495. https://doi.org/10.1007/s00521-016-2558-3

    Article  Google Scholar 

  23. Gui Z, Ge W, Yang X (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364(3–4):267–273

    Article  MATH  Google Scholar 

  24. Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  25. Yu Y (2016) Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Appl Math Comput 285:1–7. https://doi.org/10.1016/j.amc.2016.03.018

    MathSciNet  MATH  Google Scholar 

  26. Yao L (2017) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett 45(2):401–409

    Article  Google Scholar 

  27. Zhang A (2017) Pseudo almost periodic solutions for neutral type SICNNs with D operator. J Exp Theor Artif Intell 29(4):795–807

    Article  Google Scholar 

  28. Candan T (2016) Existence of positive periodic solutions of first order neutral differential equations with variable coefficients. Appl Math Lett 52:142–148

    Article  MathSciNet  MATH  Google Scholar 

  29. Yao L (2018) Global convergence of CNNs with neutral type delays and D operator. Neural Comput Appl 29(1):105–109

    Article  Google Scholar 

  30. Chen Z (2017) Global exponential stability of anti-periodic solutions for neutral type CNNs with D operator. Int J Mach Learn Cybern 9:1109–1115. https://doi.org/10.1007/s13042-016-0633-9

    Article  Google Scholar 

  31. Hilger S (1990) Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math 18(1–2):18–56

    Article  MathSciNet  MATH  Google Scholar 

  32. Bohner M, Peterson AC (eds) (2002) Advances in dynamic equations on time scales. Springer, Berlin

    Google Scholar 

  33. Agarwal RP (2002) Dynamic equations on time scales: a survey, Special Issue on “Dynamic Equations on Time Scales”, edited by RP Agarwal, M. Bohner, and D. O’Regan. Preprint in Ulmer Seminare 5:1–26

  34. Chen A, Du D (2008) Global exponential stability of delayed BAM network on time scale. Neurocomputing 71(16–18):3582–3588

    Article  Google Scholar 

  35. Li Y, Meng X, Xiong L (2017) Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales. Int J Mach Learn Cybern 8(6):1915–1927

    Article  Google Scholar 

  36. Zhou B, Song Q, Wang H (2011) Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales. Neurocomputing 74(17):3142–3150

    Article  Google Scholar 

  37. Yu X, Wang Q (2017) Weighted pseudo-almost periodic solutions for shunting inhibitory cellular neural networks on time scales. Bull Malays Math Sci Soc. https://doi.org/10.1007/s40840-017-0595-4

    Google Scholar 

  38. Zhang CY (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 151:62–76

    Article  MathSciNet  MATH  Google Scholar 

  39. Gao J, Wang QR, Zhang LW (2014) Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639–649

    MathSciNet  MATH  Google Scholar 

  40. Du B, Liu Y, Batarfi HA, Alsaadi FE (2016) Almost periodic solution for a neutral-type neural networks with distributed leakage delays on time scales. Neurocomputing 173:921–929

    Article  Google Scholar 

  41. Bohner M, Peterson A (2012) Dynamic equations on time scales: an introduction with applications. Springer, Berlin

    MATH  Google Scholar 

  42. Li Y, Yang L, Li B (2016) Existence and stability of pseudo almost periodic solution for neutral type high-order Hopfield neural networks with delays in leakage terms on time scales. Neural Process Lett 44(3):603–623

    Article  MathSciNet  Google Scholar 

  43. Wu A, Zeng Z (2016) Boundedness, Mittag–Leffler stability and asymptotical \(\omega \)-periodicity of fractional-order fuzzy neural networks. Neural Netw 74:73–84

    Article  MATH  Google Scholar 

  44. Wu A, Zhang J, Zeng Z (2011) Dynamic behaviors of a class of memristor-based Hopfield networks. Phys Lett A 375(15):1661–1665

    Article  MathSciNet  MATH  Google Scholar 

  45. Song Q, Shu H, Zhao Z, Liu Y, Alsaadi FE (2017) Lagrange stability analysis for complex-valued neural networks with leakage delay and mixed time-varying delays. Neurocomputing 244:33–41

    Article  Google Scholar 

  46. Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi FE (2018) Dynamics of complex-valued neural networks with variable coefficients and proportional delays. Neurocomputing 275:2762–2768

    Article  Google Scholar 

  47. Song Q, Yu Q, Zhao Z, Liu Y, Alsaadi FE (2018) Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties. Neural Netw 103:55–62

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chaouki Aouiti.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., Assali, E.A. & Ben Gharbia, I. Pseudo Almost Periodic Solution of Recurrent Neural Networks with D Operator on Time Scales. Neural Process Lett 50, 297–320 (2019). https://doi.org/10.1007/s11063-019-10048-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-019-10048-2

Keywords

Mathematics Subject Classification

Navigation