Abstract
This article investigates the general decay synchronization (GDS) for the bidirectional associative memory neural networks (BAMNNs). Compared with previous research results, both time-varying delays and distributed time delays are taken into consideration. By using Lyapunov method and using useful inequality techniques, some sufficient conditions on the GDS for BAMNNs are derived. Finally, a numerical example is also carried out to validate the practicability and feasibility of our proposed results. It is worth pointing out that the GDS may be specialized as exponential synchronization, polynomial synchronization and logarithmic synchronization. Besides, we can estimate the convergence rate of the synchronization by GDS. The obtained results in this article can be seen as the improvement and extension of the previously known works.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11702237, 11861063
Acknowledgments
This work was supported by the National Natural Science Foundation of China [grant number 11702237], [grant number 11861063].
-
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: This work was supported by the National Natural Science Foundation of China (grant number 11702237, 11861063).
-
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] A. Abdurahman, H. Jiang, and Z. Teng, “Finite-time synchronization for fuzzy cellular neural networks with time-varying delays,” Fuzzy Set Syst., vol. 297, pp. 96–111, 2016, https://doi.org/10.1016/j.fss.2015.07.009.Search in Google Scholar
[2] K. Shi, J. Wang, S. Zhong, Y. Tang, and J. Cheng, “Hybrid-driven finite-time sampling synchronization control for coupling memory complex networks with stochastic cyber attacks,” Neurocomputing, vol. 387, pp. 241–254, 2020, https://doi.org/10.1016/j.neucom.2020.01.022.Search in Google Scholar
[3] J. Wang, K. Shi, Q. Huang, S. Zhong, and D. Zhang, “Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout,” Appl. Math. Comput., vol. 335, pp. 211–230, 2018, https://doi.org/10.1016/j.amc.2018.04.038.Search in Google Scholar
[4] K. Shi, Y. Tang, X. Liu, and S. Zhong, “Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation,” ISA Trans., vol. 66, pp. 185–199, 2017, https://doi.org/10.1016/j.isatra.2016.11.002.Search in Google Scholar PubMed
[5] A. Wu, S. Wen, and Z. Zeng, “Synchronization control of a class of memristor-based recurrent neural networks,” Inf. Sci., vol. 183, pp. 106–116, 2012, https://doi.org/10.1016/j.ins.2011.07.044.Search in Google Scholar
[6] A. Muhammadhaji, A. Abdurahman, H. Jiang, “Finite-time synchronization of complex dynamical networks with time-varying delays and nonidentical nodes”, J. Contr. Sci. Eng., vol. 2017, 2017, p. 13, Art no. 5072308, https://doi.org/10.1155/2017/5072308.Search in Google Scholar
[7] R. Rifhat, A. Muhammadhaji, and Z. Teng, “Global mittag-leffler synchronization for impulsive fractional-order neural networks with delays,” Int. J. Nonlin. Sci. Numer. Simul., vol. 19, nos. 2–3, pp. 205–213, 2018, https://doi.org/10.1515/ijnsns-2017-0179.Search in Google Scholar
[8] K. Shi, J. Wang, Y. Tang, and S. Zhong, “Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies,” Fuzzy Set Syst., vol. 381, pp. 1–25, 2020, https://doi.org/10.1016/j.fss.2018.11.017.Search in Google Scholar
[9] J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays,” IEEE Trans. Neural Netw., vol. 13, no. 2, pp. 457–63, 2002.10.1109/72.991431Search in Google Scholar PubMed
[10] B. Kosko, “Bidirectional associative memories,” IEEE Trans. Syst. Man Cybern., vol. 18, no. 1, pp. 49–60, 1988, https://doi.org/10.1109/21.87054.Search in Google Scholar
[11] J. H. Park, “A novel criterion for global asymptotic stability of BAM neural networks with time delays,” Chaos, Solit. Fract., vol. 29, no. 2, pp. 446–453, 2006, https://doi.org/10.1016/j.chaos.2005.08.018.Search in Google Scholar
[12] J. Ge and J. Xu, “Synchronization and synchronized periodic solution in a simplified fiveneuron BAM neural networks with delays,” Neurocomputing, vol. 74, pp. 993–999, 2011, https://doi.org/10.1016/j.neucom.2010.11.017.Search in Google Scholar
[13] F. Zhou and C. Ma, “Global Exponential Stability of high-order BAM neural networks with reaction-diffusion terms,” Int. J. Bifurcat. Chaos, vol. 10, pp. 3209–3223, 2010, https://doi.org/10.1142/s0218127410027635.Search in Google Scholar
[14] Y. Li and C. Li, “Matrix measure strategies for stabilization and synchronization of delayed BAM neural networks,” Nonlinear Dynam., vol. 84, no. 3, pp. 1759–1770, 2016, https://doi.org/10.1007/s11071-016-2603-x.Search in Google Scholar
[15] J. Cao and Y. Wan, “Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays,” Neural Netw., vol. 53, pp. 165–172, 2014, https://doi.org/10.1016/j.neunet.2014.02.003.Search in Google Scholar PubMed
[16] W. Wang, X. Wang, X. Luo, and M. Yuan, “Finite-time projective synchronization of memristor-based BAM neural networks and applications in image encryption,” IEEE Access, vol. 6, pp. 56457–56476, 2018, https://doi.org/10.1109/access.2018.2872745.Search in Google Scholar
[17] F. Zhou, “Global exponential synchronization of a class of BAM neural networks with time-varying delays,” WSEAS Trans. Math., vol. 12, no. 2, pp. 138–148, 2013.Search in Google Scholar
[18] R. Tang, X. Yang, X. Wan, Y. Zou, Z Cheng, M. F. Habib, “Finite-time synchronization of nonidentical BAM discontinuous fuzzy neural networks with delays and impulsive effects via non-chattering quantized control,” Commun. Nonlinear Sci. Numer. Simul., vol. 78, 2019, Art no. 104893, https://doi.org/10.1016/j.cnsns.2019.104893.Search in Google Scholar
[19] C. Chen, L. Li, H. Peng, and Y. Yang, “Fixed-time synchronization of memristor-based BAM neural networks with time-varying discrete delay,” Neural Netw., vol. 96, pp. 47–54, 2017, https://doi.org/10.1016/j.neunet.2017.08.012.Search in Google Scholar PubMed
[20] K. Mathiyalagan, J. H. Park, and R. Sakthivel, “Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities,” Appl. Math. Comput., vol. 259, pp. 967–979, 2015, https://doi.org/10.1016/j.amc.2015.03.022.Search in Google Scholar
[21] J. Xiao, S. Zhong, Y. Li, and F. Xu, “Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays,” Neurocomputing, vol. 219, pp. 431–439, 2017, https://doi.org/10.1016/j.neucom.2016.09.049.Search in Google Scholar
[22] D. Wang, L. Huang, and L. Tang, “Dissipativity and synchronization of generalized BAM neural networks with multivariate discontinuous activations,” IEEE Trans. Neural Netw. Learn. Syst., 2017, https://doi.org/10.1109/TNNLS.2017.2741349.Search in Google Scholar PubMed
[23] M. Sader, A. Abdurahman, and H. Jiang, “General decay synchronization of delayed BAM neural networks via nonlinear feedback control,” Appl. Math. Comput., vol. 337, pp. 302–314, 2018, https://doi.org/10.1016/j.amc.2018.05.046.Search in Google Scholar
[24] L. Wang, Y Shen, and G. Zhang, “Synchronization of a class of switched neural networks with time-varying delays via nonlinear feedback control,” IEEE Trans. Cybern., vol. 46, no. 10, pp. 2300–2310, 2016, https://doi.org/10.1109/tcyb.2015.2475277.Search in Google Scholar PubMed
[25] L. Wang, Y. Shen, and G. Zhang, “General decay synchronization stability for a class of delayed chaotic neural networks with discontinuous activations,” Neurocomputing, vol. 179, pp. 169–175, 2016, https://doi.org/10.1016/j.neucom.2015.11.077.Search in Google Scholar
[26] A. Muhammadhaji and A. Halik, “Synchronization stability for recurrent neural networks with time-varying delays,” Sci. Asia, vol. 45, pp. 179–186, 2019, https://doi.org/10.2306/scienceasia1513-1874.2019.45.179.Search in Google Scholar
[27] A. Muhammadhaji and Z. Teng, “General decay synchronization for recurrent neural networks with mixed time delays,” J. Syst. Sci. Complex., vol. 33, pp. 672–684, 2020, https://doi.org/10.1007/s11424-020-8209-x.Search in Google Scholar
[28] A. Muhammadhaji and A. Abdurahman, “General decay synchronization for fuzzy cellular neural networks with time-varying delays,” Int. J. Nonlinear Sci. Numer. Simul., vol. 20, no. 5, pp. 551–560, 2019, https://doi.org/10.1515/ijnsns-2018-0041.Search in Google Scholar
[29] M. Zheng, L. Li, H. Peng, J. Xiao, Y. Yang, Y. Zhang, and H. Zhao, “General decay synchronization of complex multi-links time-varying dynamic network,” Commun. Nonlinear Sci. Numer. Simul., vol. 67, pp. 108–123, 2019, https://doi.org/10.1016/j.cnsns.2018.06.015.Search in Google Scholar
[30] A. Abdurahman, H. jiang, and C. Hu, “General decay synchronization of memristor-based Cohen-Grossberg neural networks with mixed time-delays and discontinuous activations,” J. Franklin Inst., vol. 354, pp. 7028–7052, 2017, https://doi.org/10.1016/j.jfranklin.2017.08.013.Search in Google Scholar
[31] M. Sader, A. Abdurahman, and H. Jiang, “General decay Lag synchronization for competitive neural networks with constant delays,” Neural Process. Lett., vol. 50, no. 1, pp. 445–457, 2019, https://doi.org/10.1007/s11063-019-09984-w.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
