General decay projective synchronization of memristive competitive neural networks via nonlinear controller

Malika Sader; Fuyong Wang; Zhongxin Liu; Zengqiang Chen

doi:10.1515/ijnsns-2020-0037

Article

General decay projective synchronization of memristive competitive neural networks via nonlinear controller

Malika Sader , Fuyong Wang , Zhongxin Liu and Zengqiang Chen

Published/Copyright: December 6, 2021

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From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 23 Issue 6

Abstract

In this paper, the general decay projective synchronization of a class of memristive competitive neural networks with time delay is studied. Firstly, a nonlinear feedback controller is designed, which does not require any knowledge about the activation functions. Then, some new and applicable conditions dependent on the Lyapunov function and the inequality techniques are obtained to guarantee the general decay projective synchronization of the considered systems under the developed controller. Unlike other forms of synchronization, projective synchronization can improve communication security due to the scaling constant’s unpredictability. In addition, the polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen as the special cases of the general decay projective synchronization. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control scheme.

Keywords: competitive neural networks; general decay projective synchronization; nonlinear feedback controller; time delays

Corresponding author: Zhongxin Liu, College of Artificial Intelligence, Nankai University, Tianjin 300350, China, E-mail: lzhx@nankai.edu.cn

Funding source: Tianjin Postgraduate Scientific Research and Innovation Project

Award Identifier / Grant number: 2020YJSZXB03

Award Identifier / Grant number: 2020YJSZXB12

Funding source: National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809

Award Identifier / Grant number: 61973175

Award Identifier / Grant number: No. 61573200, 61973175

Funding source: Tianjin Natural Science Foundation of China

Award Identifier / Grant number: 20JCQNJC01450

Award Identifier / Grant number: 20JCYBJC01060

Acknowledgement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This work is supported by the Tianjin Natural Science Foundation of China (Grant No. 20JCYBJC01060, 20JCQNJC01450), the National Natural Science Foundation of China (Grant No. 61973175), the Tianjin Postgraduate Scientific Research and Innovation Project (Grant No. 2020YJSZXB03, 2020YJSZXB12).
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] C. Hu, J. Yu, Z. Chen, H. Jiang, and T. Huang, “Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks,” Neural Network., vol. 89, pp. 74–83, 2017. https://doi.org/10.1016/j.neunet.2017.02.001.Search in Google Scholar PubMed

[2] X. Liu and T. Chen, “Finite-time and fixed-time cluster synchronization with or without pinning control,” IEEE Trans. Cybern., vol. 48, pp. 240–252, 2018. https://doi.org/10.1109/tcyb.2016.2630703.Search in Google Scholar PubMed

[3] L. Wang, Z. Zeng, J. Hu, and X. Wang, “Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations,” Neural Network., vol. 87, pp. 122–131, 2017. https://doi.org/10.1016/j.neunet.2016.12.006.Search in Google Scholar PubMed

[4] N. Wang, X. Li, and J. Lu, “Impulsive-interaction-driven synchronization in an array of coupled neural networks,” Neural Process. Lett., vol. 51, pp. 2685–2700, 2020. https://doi.org/10.1007/s11063-020-10214-x.Search in Google Scholar

[5] W. Wu, L. Yang, and Y. Ren, “Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 22, no. 1, pp. 13–21, 2021. https://doi.org/10.1515/ijnsns-2019-0142.Search in Google Scholar

[6] T. Hu, X. Zhang, and S. Zhong, “Global asymptotic synchronization of nonidentical fractional-order neural networks,” Neurocomputing, vol. 313, no. 3, pp. 39–46, 2018. https://doi.org/10.1016/j.neucom.2018.05.098.Search in Google Scholar

[7] A. Muhammadhaji and Z. D. Teng, “Synchronization stability on the BAM neural networks with mixed time delays,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 22, no. 1, pp. 99–109, 2021. https://doi.org/10.1515/ijnsns-2019-0308.Search in Google Scholar

[8] Y. Shi and P. Zhu, “Synchronization of memristive competitive neural networks with different time scales,” Neural Comput. Appl., vol. 25, no. 5, pp. 1163–1168, 2014. https://doi.org/10.1007/s00521-014-1598-9.Search in Google Scholar

[9] L. Chua, “Memristor - the missing circuit element,” IEEE Trans. Circ. Theor., vol. 18, no. 5, pp. 507–519, 1971. https://doi.org/10.1109/tct.1971.1083337.Search in Google Scholar

[10] D. Soudry, D. D. Castro, A. Gal, A. Kolodny, and S. Kvatinsky, “Memristor-based multilayer neural networks with online gradient descent training,” IEEE Trans. Neural Network. Learn. Syst., vol. 26, no. 10, pp. 2408–2421, 2017. https://doi.org/10.1109/TNNLS.2014.2383395.Search in Google Scholar PubMed

[11] T. Greenberg-Toledo, R. Mazor, A. Haj-Ali, and S. Kvatinsky, “Supporting the momentum training algorithm using a memristor-based synapse,” IEEE Trans. Circuits Syst. I, vol. 66, no. 4, pp. 1571–1583, 2019. https://doi.org/10.1109/tcsi.2018.2888538.Search in Google Scholar

[12] Y. Pershin and M. Ventra, “Experimental demonstration of associative memory with memristive neural networks,” Neural Network., vol. 23, pp. 881–886, 2010. https://doi.org/10.1016/j.neunet.2010.05.001.Search in Google Scholar PubMed

[13] Y. Ho, G. Huang, and P. Li, “Dynamical properties and design analysis for nonvolatile memristor memories,” IEEE Trans. Circuits Syst. I, vol. 58, no. 4, pp. 724–736, 2011. https://doi.org/10.1109/tcsi.2010.2078710.Search in Google Scholar

[14] H. Bao and J. Cao, “Projective synchronization of fractional-order memristor-based neural networks,” Neural Network., vol. 63, pp. 1–9, 2015. https://doi.org/10.1016/j.neunet.2014.10.007.Search in Google Scholar PubMed

[15] S. Gong, S. Yang, Z. Guo, and T. Huang, “Global exponential synchronization of memristive competitive neural networks with time-varying delay via nonlinear control,” Neural Process. Lett., vol. 49, no. 1, pp. 103–119, 2019. https://doi.org/10.1007/s11063-017-9777-1.Search in Google Scholar

[16] Q. Gan, “Synchronization of competitive neural networks with different time scales and time-varying delay based on delay partitioning approach,” Int. J. Mach. Learn. Cybern., vol. 4, no. 4, pp. 327–337, 2013. https://doi.org/10.1007/s13042-012-0097-5.Search in Google Scholar

[17] Q. Gan, R. Xu, and X. Kang, “Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification,” Nonlinear Dynam., vol. 67, no. 3, pp. 1893–1902, 2012. https://doi.org/10.1007/s11071-011-0116-1.Search in Google Scholar

[18] Y. Shi and P. Zhu, “Synchronization of stochastic competitive neural networks with different timescales and reaction–diffusion terms,” Neural Comput., vol. 26, no. 9, pp. 2005–2024, 2014. https://doi.org/10.1162/neco_a_00629.Search in Google Scholar

[19] F. Li and X. Lu, “Complete synchronization of temporal Boolean networks,” Neural Network., vol. 44, pp. 72–77, 2013. https://doi.org/10.1016/j.neunet.2013.03.009.Search in Google Scholar PubMed

[20] 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

[21] X. Liu, K. Zhang, and W. C. Xie, “Pinning impulsive synchronization of reaction–diffusion neural networks with time-varying delays,” IEEE Trans. Neural Network. Learn. Syst., vol. 28, no. 5, pp. 1055–1067, 2017. https://doi.org/10.1109/tnnls.2016.2518479.Search in Google Scholar PubMed

[22] D. Wang, L. Huang, L. Tang, and J. Zhuang, “Generalized pinning synchronization of delayed Cohen–Grossberg neural networks with discontinuous activations,” Neural Network., vol. 104, pp. 80–92, 2018. https://doi.org/10.1016/j.neunet.2018.04.006.Search in Google Scholar PubMed

[23] C. Chen, L. Li, H. Peng, Y. Yang, L. Mi, and B. Qiu, “Fixed-time projective synchronization of memristive neural networks with discrete delay,” Physica A, vol. 534, no. 15, p. 122248, 2019. https://doi.org/10.1016/j.physa.2019.122248.Search in Google Scholar

[24] A. Abdurahman, M. Sader, and H. Jiang, “Improved results on adaptive control approach for projective synchronization of neural networks with time-varying delay,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 20, no. 6, pp. 623–631, 2019. https://doi.org/10.1515/ijnsns-2018-0002.Search in Google Scholar

[25] J. Yu, C. Hu, H. Jiang, and X. Fan, “Projective synchronization for fractional neural networks,” Neural Network., vol. 49, pp. 87–95, 2014. https://doi.org/10.1016/j.neunet.2013.10.002.Search in Google Scholar PubMed

[26] M. Sader, F. Wang, Z. Liu, and Z. Chen, “Projective synchronization analysis for BAM neural networks with time-varying delay via novel control,” Nonlinear Anal. Model Control, vol. 26, no. 1, pp. 41–56, 2014. https://doi.org/10.15388/namc.2021.26.21204.Search in Google Scholar

[27] A. Anber, Z. Dahmani, and B. Bendoukha, “Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller,” Appl. Math. Comput., vol. 217, pp. 164–174, 2010.10.1016/j.amc.2010.05.037Search in Google Scholar

[28] A. Abdurahman and H. Jiang, “Nonlinear control scheme for general decay projective synchronization of delayed memristor-based BAM neural networks,” Neurocomputing, vol. 357, pp. 282–291, 2019. https://doi.org/10.1016/j.neucom.2019.05.015.Search in Google Scholar

[29] L. Hien, V. Phat, and H. Trinh, “New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems,” Nonlinear Dynam., vol. 82, pp. 1–13, 2015. https://doi.org/10.1007/s11071-015-2176-0.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, no. 15, pp. 7028–7052, 2017. https://doi.org/10.1016/j.jfranklin.2017.08.013.Search in Google Scholar

[31] L. Zhang, Y. Yang, and F. Wang, “Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch,” Physica A, vol. 471, pp. 402–415, 2017. https://doi.org/10.1016/j.physa.2016.12.030.Search in Google Scholar

[32] 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

Received: 2020-02-23

Revised: 2021-02-22

Accepted: 2021-11-04

Published Online: 2021-12-06

Published in Print: 2022-10-27

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Articles in the same Issue

https://doi.org/10.1515/ijnsns-2020-0037

Keywords for this article

competitive neural networks; general decay projective synchronization; nonlinear feedback controller; time delays