Research ArticleNo Access

Global exponential $p$ $p$ -norm stability of BAM neural networks with unbounded time-varying delays: A method based on the representation of solutions

School of Mathematical Science, Heilongjiang University, No. 74 Xuefu Road, Harbin 150080, P. R. China

E-mail Address: 532037566@qq.com

School of Mathematical Science, Heilongjiang University, No. 74 Xuefu Road, Harbin 150080, P. R. China

Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, No. 74 Xuefu Road, Harbin 150080, P. R. China

E-mail Address: tingtingyu@hlju.edu.cn

Corresponding authors.

Search for more papers by this author

, and

Xian Zhang

https://orcid.org/0000-0001-7023-7351

School of Mathematical Science, Heilongjiang University, No. 74 Xuefu Road, Harbin 150080, P. R. China

Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, No. 74 Xuefu Road, Harbin 150080, P. R. China

E-mail Address: xianzhang@hlju.edu.cn

Corresponding authors.

Search for more papers by this author

https://doi.org/10.1142/S1793524522501054Cited by:4 (Source: Crossref)

Abstract

This paper studies the global exponential $p$ $p$ -norm stability of bidirectional associative memory (BAM) neural networks with unbounded time-varying delays. A novel method based on the representation of solutions is put forward to deduce a global exponential $p$ $p$ -norm stability criterion. This method does not need to set up any Lyapunov–Krasovskii functionals (LKF), which can greatly reduce a large amount of computations and is simpler than the existing methods. In the end, representative numerical examples are given to illustrate the availability of the method.

Keywords:

Remember to check out the Most Cited Articles in IJB!

Check out new Biomathematics books in our Mathematics 2018 catalogue!
Featuring author Frederic Y M Wan and more!

References

1. C. Aouiti and M. B. Rezeg, Impulsive multidirectional associative memory neural networks: New results, Int. J. Biomath. 14(7) (2021) 2150060. Link, Web of Science, Google Scholar
2. Y. Chen, S. Huang, J. Yin and Q. Li, Novel global exponential stability analysis for BAM neural networks with time-varying delays, in Proc. 21st Chinese Control and Decision Conf. (CCDC) (IEEE, 2009), pp. 4355–4360. Crossref, Google Scholar
3. Y. Chen and T. Qin, Improved global exponential stability criterion for BAM neural networks with time-varying delays, in Proc. 5th Int. Symp. Neural Networks (ISNN), Part I (Springer, 2008), pp. 128–137. Crossref, Google Scholar
4. Z. Dong, X. Wang and X. Zhang, A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks, Appl. Math. Comput. 385 (2020) 125401. Web of Science, Google Scholar
5. Z. Dong, X. Zhang and X. Wang, State estimation for discrete-time high-order neural networks with time-varying delays, Neurocomputing 411 (2020) 282–290. Crossref, Web of Science, Google Scholar
6. Z. Dong, X. Zhang and X. Wang, Global exponential stability of discrete-time higher-order Cohen–Grossberg neural networks with time-varying delays, connection weights and impulses, J. Franklin Inst. 358(11) (2021) 5931–5950. Crossref, Web of Science, Google Scholar
7. D. W. C. Ho, J. Liang and J. Lam, Global exponential stability of impulsive high-order BAM neural networks with time-varying delays, Neural Netw. 19(10) (2006) 1581–1590. Crossref, Web of Science, Google Scholar
8. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA 79(8) (1982) 2554–2558. Crossref, Web of Science, Google Scholar
9. L. Hu, H. Liu and Y. Zhao, New stability criteria for BAM neural networks with time-varying delays Neurocomputing 72(13–15) (2009) 3245–3252. Crossref, Web of Science, Google Scholar
10. B. Kosko, Adaptive bidirectional associative memories, Appl. Opt. 26(23) (1987) 4947–4960. Crossref, Web of Science, Google Scholar
11. H. Li, H. Jiang and C. Hu, Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural Netw. 75 (2016) 97–109. Crossref, Web of Science, Google Scholar
12. B. Liu, Global exponential stability for BAM neural networks with time-varying delays in the leakage terms, Nonlinear Anal. Real World Appl. 14(1) (2013) 559–566. Crossref, Web of Science, Google Scholar
13. X. Meng, X. Zhang, Y. Wang and C. Liu, A representation of system solutions for global exponential stabilization of memristor-based neural networks with unbounded time-varying delays, IEEE Access 9 (2021) 118107–118112. Crossref, Web of Science, Google Scholar
14. Ju H. Park, S. M. Lee and O. M. Kwon, On exponential stability of bidirectional associative memory neural networks with time-varying delays, Chaos Solitons Fractals 39 (2009) 1083–1091. Crossref, Web of Science, Google Scholar
15. C.-A. Popa, Global $μ$ $μ$ -stability of neutral-type impulsive complex-valued BAM neural networks with leakage delay and unbounded time-varying delays, Neurocomputing 376 (2020) 73–94. Crossref, Web of Science, Google Scholar
16. B. Priya, M. Syed Ali, G. K. Thakur, S. Sanober and B. Dhupia, $p$ $p$ -th moment exponential stability of memristor Cohen–Grossberg BAM neural networks with time-varying delays and reaction–diffusion, Chin. J. Phys. 21 (2021) 1–16. Google Scholar
17. V. Scholz, P. Winkler, A. Hornig, M. Gude and A. Filippatos, Structural damage identification of composite rotors based on fully connected neural networks and convolutional neural networks, Science 21(6) (2021) 2005. Google Scholar
18. H. Shen, X. Hu, J. Wang, J. Cao and W. Qian, Non-fragile $H_{\infty}$ $H_{\infty}$ synchronization for Markov jump singularly perturbed coupled neural networks subject to double-layer switching regulation, IEEE Trans. Neural Netw. Learn. Syst., 2021, https://doi.org/10.1109/TNNLS.2021.3107607. Web of Science, Google Scholar
19. H. Shen, Z. Huang, Z. Wu, J. Cao and Ju H. Park, Nonfragile $H_{\infty}$ $H_{\infty}$ synchronization of BAM inertial neural networks subject to persistent dwell-time switching regularity. IEEE Trans. Cybern. 2021, https://doi.org/10.1109/TCYB.2021.3119199. Web of Science, Google Scholar
20. S. K. Thangarajan and A. Chokkalingam, Integration of optimized neural network and convolutional neural network for automated brain tumor detection, Sensor Rev. 41(1) (2021) 16–34. Crossref, Web of Science, Google Scholar
21. J. Thipcha and P. Niamsup, Global exponential stability criteria for bidirectional associative memory neural networks with time-varying delays, Abstr. Appl. Anal. 2013 (2013) 576721. Crossref, Google Scholar
22. N. Mohamed Thoiyab, P. Muruganantham, Q. Zhu and N. Gunasekaran, Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties. Chaos Solitons Fractals 152 (2021) 111441. Crossref, Web of Science, Google Scholar
23. S. C. Tong, Y. M. Li and H.-G. Zhang, Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays, IEEE Trans. Neural Netw. 22(7) (2011) 21073–1086. Google Scholar
24. J. Townsend, T. Chaton and J. M. Monteiro, Extracting relational explanations from deep neural networks: A survey from a neural-symbolic perspective, IEEE Trans. Neural Netw. Learn. Syst. 31(9) (2020) 3456–3470. Crossref, Web of Science, Google Scholar
25. H. Wang, Q. Songb and C. Duan, LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions, Math. Comput. Simul. 81 (2010) 837–850. Crossref, Web of Science, Google Scholar
26. J. Wang, J. Xia, H. Shen, M. Xing and J. H. Park, $ℋ_{\infty}$ synchronization for fuzzy Markov jump chaotic systems with piecewise-constant transition probabilities subject to PDT switching rule, IEEE Trans. Fuzzy Syst. 29(10) (2021) 3082–3092. Crossref, Web of Science, Google Scholar
27. T. Wang and Q. Zhu, Stability analysis of stochastic BAM neural networks with reaction-diffusion, multi-proportional and distributed delays, Physica A 533 (2019) 121935. Crossref, Web of Science, Google Scholar
28. J. Xiao, S. Wen, X. Yang and S. Zhong, New approach to global Mittag-Leffler synchronization problem of fractional-order quaternion-valued BAM neural networks based on a new inequality, Neural Netw. 122 (2020) 320–337. Crossref, Web of Science, Google Scholar
29. L. Xing and L. Zhou, Polynomial dissipativity of proportional delayed BAM neural networks, Int. J. Biomath. 13(6) (2020) 2050050. Link, Google Scholar
30. C. Xu, P. Li and Y. Pang, Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays, Math. Method. Appl. Sci. 39(18) (2016) 5720–5731. Crossref, Web of Science, Google Scholar
31. Y. Xue, C. Liu and X. Zhang, State bounding description and reachable set estimation for discrete-time genetic regulatory networks with time-varying delays and bounded disturbances, IEEE Trans. Syst. Man Cybern. Syst. 2022, https://doi.org/10.1109/TSMC.2022.3148715. Crossref, Web of Science, Google Scholar
32. T. Yu, S. Liu, H. Wang, Y. Cui and D. Cao, Robust delay-dependent stability of uncertain inertial neural networks with impulsive effects and distributed-delay, Int. J. Biomath. 12(1) (2019) 1950010. Link, Google Scholar
33. L. Zhang and Y. Yang, Finite time impulsive synchronization of fractional order memristive BAM neural networks, Neurocomputing 384 (2020) 213–224. Crossref, Web of Science, Google Scholar
34. X. Zhang, Y. Wang and X. Wang, A direct parameterized approach to global exponential stability of neutral-type Cohen–Grossberg neural networks with multiple discrete and neutral delays, Neurocomputing 463 (2021) 334–340. Crossref, Web of Science, Google Scholar
35. Z. Zhang, Y. Yang and Y. Huang, Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays, Neural Netw. 24 (2011) 457–465. Crossref, Web of Science, Google Scholar
36. J. Zhao, Exponential stabilization of memristor-based neural networks with unbounded time-varying delays, Sci. China-Inf. Sci. 64(8) (2021) 189205. Crossref, Web of Science, Google Scholar
37. Z. Zhao, F. Liu, X. Xie, X. Liu and Z. Tang, Asymptotic stability of bidirectional associative memory neural networks with time-varying delays via delta operator approach, Neurocomputing 117 (2013) 40–46. Crossref, Web of Science, Google Scholar
38. L. Zhou, Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays, Neurocomputing 161 (2015) 99–106. Crossref, Web of Science, Google Scholar
39. J. Zu, Z. Yu and Y. Meng, Global exponential stability of high-order bidirectional associative memory (BAM) neural networks with proportional delays, Neural Process. Lett. 51(3) (2020) 2531–2549. Crossref, Web of Science, Google Scholar