Skip to main content
Log in

On the Weighted Pseudo-Almost Periodic Solution for BAM Networks with Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, a class of Bidirectional Associative Memory neural networks with time-varying weights and continuously distributed delays is discussed. Sufficient conditions are obtained for the existence and uniqueness of weighted pseudo-almost periodic solution of the considered model and numerical examples are given to show the effectiveness of the obtained results.

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.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Ammar B, Chérif F, Alimi AM (2012) Existence and uniqueness of pseudo-almost periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Trans Neural Netw 23(1):109–118

    Article  Google Scholar 

  2. Ammar B, Chouikhi N, Alimi AM, Chérif F, Rezzoug N, Gorce P (2013) Learning to walk using a recurrent neural network with time delay. Artificial neural networks and machine learning (ICANN), pp. 511–518

    Chapter  Google Scholar 

  3. Arbi A, Aouiti C, Chérif F, Touati A, Alimi AM (2015) Stability analysis of delayed Hopfield neural networks with impulses via inequality techniques. Neurocomputing 158:281–294

    Article  Google Scholar 

  4. Arik S (2005) Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays. IEEE Trans Neural Netw 16(3):580–586

    Article  Google Scholar 

  5. Bart K (1992) Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence/book and disk, vol 1. Prentice hall, Upper Saddle River

    MATH  Google Scholar 

  6. Brahmi H, Ammar B, Cherif F, Alimi AM (2014) On the dynamics of the high-order type of neural networks with time varying coefficients and mixed delay. In: IEEE international joint conference on neural networks, pp. 2063–2070

  7. Brahmi H, Ammar B, Chérif F, Alimi AM (2016) Stability and exponential synchronization of high-order hopfield neural networks with mixed delays. Cybern Syst 1–21

  8. Brahmi H, Ammar B, Cherif F, Alimi AM (2016) Pseudo almost periodic solutions of impulsive recurrent neural networks with mixed delays. In: International joint conference on neural networks (IJCNN), Vancouver, BC, pp. 464–470

  9. Brahmi H, Ammar B, Alimi AM (2013) Intelligent path planning algorithm for autonomous robot based on recurrent neural networks. In: International conference on advanced logistics and transport (ICALT), pp. 199–204

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

    Article  Google Scholar 

  11. Chen A, Chen F (2009) Periodic solution to BAM neural network with delays on time scales. Neurocomputing 73(1–3):274–282

    Article  Google Scholar 

  12. Chérif F (2011) A various types of almost periodic functions on banach spaces: part 1. Int Math Forum 6(19):921–952

    MathSciNet  MATH  Google Scholar 

  13. Chérif F (2012) Existence and global exponential stability of pseudo almost periodic solution for SICNNs with mixed delays. J Appl Math Comput Numbers 39(1–2):235–251

    Article  MathSciNet  Google Scholar 

  14. Chouikhi N, Ammar B, Rokbani N, Alimi AM (2017) PSO-based analysis of Echo State Network parameters for time series forecasting. Appl Soft Comput 55:211–225

    Article  Google Scholar 

  15. Corduneanu C (1968) Almost periodic functions. Wiley, New York

    MATH  Google Scholar 

  16. Desheng J, Zhang C (2012) Translation invariance of weighted pseudo almost periodic functions and related problems. J Math Anal Appl 391(2):350–362

    Article  MathSciNet  Google Scholar 

  17. Fukada T, Schuster M, Sagisaka Y (1999) Phoneme boundary estimation using bidirectional recurrent neural networks and its applications. Syst Comput Japan 30(4):20–30

    Article  Google Scholar 

  18. Blot J, Cieutat P, Ezzinbi K (2013) New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications. Appl Anal 92(3):493–526

    Article  MathSciNet  Google Scholar 

  19. Hamid AJ, Brahim RW (2009) Almost-periodic solution for BAM neural network. Surv Math Appl 4:53–63

    MathSciNet  Google Scholar 

  20. Kosko B (1987) Adaptive bi-directional associative memories. Appl Optim 26(23):4947–4960

    Article  Google Scholar 

  21. Li G, Li B, Yu X, Cheng C (2015) Echo state Network with Bayesian regularization for forecasting short-term power production of small hydropower plants. J Energies 8(10):12228–12241

    Article  Google Scholar 

  22. Li H, Jiang H, Hu C (2016) Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays. Neural Netw 75:97–109

    Article  Google Scholar 

  23. Liao X, Yang S, Wong K (2003) Convergence analysis of hybrid bi-directional associative memory neural networks with discrete delays. Int J Dyn Syst 18(3):231–243

    Article  MathSciNet  Google Scholar 

  24. Liu Y, Tang W (2006) Existence and global exponential stability of periodic solutions of BAM neural networks with periodic coefficients and delays. Neurocomputing 69(Issues 16–18):2152–2160

    Article  Google Scholar 

  25. Liu B (2007) Existence and exponential stability of almost periodic solutions for cellular neural networks without global Lipschitz conditions. J Korean Math Soc 44(4):873–887

    Article  MathSciNet  Google Scholar 

  26. Quanxin Z, Rakkiyappan R, Chandrasekar A (2014) Stochastic stability of Markovian jump BAM neural networks with leakage delays and impulse control. Neurocomputing 136:136–151

    Article  Google Scholar 

  27. Saad E, Prokhorov D, Wunsch D (2002) Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks. In: IEEE Transactions on neural networks, p 1456

    Article  Google Scholar 

  28. Schuster M, Paliwal KK (1997) Bidirectional recurrent neural networks. IEEE Trans Signal Process 45:2673

    Article  Google Scholar 

  29. Shaohong C, Zhang Q (2016) Existence and stability of periodic solutions for impulsive fuzzy BAM Cohen–Grossberg neural networks on time scales. Adv Differ Equ 1–21

  30. Singh M, Kumar S (2013) Using multi-layered feed-forward neural network (MLFNN) architecture as bidirectional associative memory (BAM) for function approximation. IOSR J Comput Eng 13(4):34–38

    Article  Google Scholar 

  31. Song Q, Cao J (2007) Global exponential stability of bidirectional associative memory neural networks with distributed delays. J Comput Appl Math 202:266–279

    Article  MathSciNet  Google Scholar 

  32. Xu Y (2017) Exponential stability of pseudo almost periodic solutions for neutral type cellular neural networks with D operator. Neural Process Lett 46(1):329

    Article  Google Scholar 

  33. Xu C, Li, P (2016) Exponential stability for fuzzy BAM cellular neural networks with distributed leakage delays and impulses. Adv Differ Equ 276

  34. Xu CJ, Li PL (2016) Existence and exponentially stability of anti-periodic solutions for neutral BAM neural networks with time-varying delays in the leakage terms. J Nonlinear Sci Appl 9(3):1285–1305

    Article  MathSciNet  Google Scholar 

  35. Zhang QH, Yang LH (2012) Dynamical analysis of fuzzy BAM neural networks with variable delays. Fuzzy Inf Eng 4(1):93–104

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the financial support of this work by grants from General Direction of Scientific Research (DGRST), Tunisia, under the ARUB program.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Boudour Ammar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ammar, B., Brahmi, H. & Chérif, F. On the Weighted Pseudo-Almost Periodic Solution for BAM Networks with Delays. Neural Process Lett 48, 849–862 (2018). https://doi.org/10.1007/s11063-017-9725-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-017-9725-0

Keywords

Navigation