Synchronization robustness analysis of memristive-based neural networks with deviating arguments and stochastic perturbations

Tao Xie; Xing Xiong; Qike Zhang; Tao Xie; Xing Xiong; Qike Zhang

doi:10.3934/math.2024046

AIMS Mathematics

2024, Volume 9, Issue 1: 918-941. doi: 10.3934/math.2024046

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Synchronization robustness analysis of memristive-based neural networks with deviating arguments and stochastic perturbations

School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

Received: 10 October 2023 Revised: 14 November 2023 Accepted: 23 November 2023 Published: 04 December 2023
MSC : 93B35, 93D23

In this article, we investigate the robustness of memristive-based neural networks (MNNs) with deviating arguments (DAs) and stochastic perturbations (SPs). Based on the set-valued mapping method, differential inclusion theory and Gronwall inequalities, we derive the upper bounds for the width of DAs and the intensity of SPs. When the DAs and SPs are smaller than these upper bounds, the MNNs maintains exponential synchronization. Finally, several specific simulation examples demonstrate the effectiveness of the results.
- memristive-based neural networks,
- deviating arguments,
- stochastic perturbations,
- exponential synchronization
Citation: Tao Xie, Xing Xiong, Qike Zhang. Synchronization robustness analysis of memristive-based neural networks with deviating arguments and stochastic perturbations[J]. AIMS Mathematics, 2024, 9(1): 918-941. doi: 10.3934/math.2024046

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Abstract

In this article, we investigate the robustness of memristive-based neural networks (MNNs) with deviating arguments (DAs) and stochastic perturbations (SPs). Based on the set-valued mapping method, differential inclusion theory and Gronwall inequalities, we derive the upper bounds for the width of DAs and the intensity of SPs. When the DAs and SPs are smaller than these upper bounds, the MNNs maintains exponential synchronization. Finally, several specific simulation examples demonstrate the effectiveness of the results.

References

[1]	L. Chua, Memristor-the missing circuit element, IEEE T. Circuits-Theor., 18 (1971), 507–519. https://doi.org/10.1109/TCT.1971.1083337 doi: 10.1109/TCT.1971.1083337
[2]	D. B. Strukov, G. S. Snider, D. R. Stewart, R. S. Williams, The missing memristor found, Nature, 453 (2008), 80–83. https://doi.org/10.1038/nature06932 doi: 10.1038/nature06932
[3]	X. Huang, Y. Fan, J. Jia, Z. Wang, Y. Li, Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches, IET Control Theory A., 11 (2017), 2317–2327. https://doi.org/10.1049/iet-cta.2017.0196 doi: 10.1049/iet-cta.2017.0196
[4]	H. Bao, J. H. Park, J. Cao, Adaptive synchronization of fractional-order memristor-based neural networks with time delay, Nonlinear Dynam., 82 (2015), 1343–1354. https://doi.org/10.1007/s11071-015-2242-7 doi: 10.1007/s11071-015-2242-7
[5]	F. Du, J. G. Lu, New criteria for finite-time stability of fractional order memristor-based neural networks with time delays, Neural Comput., 421 (2021), 349–359. https://doi.org/10.1016/j.neucom.2020.09.039 doi: 10.1016/j.neucom.2020.09.039
[6]	L. Wang, Y. Shen, Q. Yin, G. Zhang, Adaptive synchronization of memristor-based neural networks with time-varying delays, IEEE T. Neural Net. Lear., 26 (2014), 2033–2042. https://doi.org/10.1109/TNNLS.2014.2361776 doi: 10.1109/TNNLS.2014.2361776
[7]	C. Yang, L. Huang, Z. Cai, Fixed-time synchronization of coupled memristor-based neural networks with time-varying delays, Neural Networks, 116 (2019), 101–109. https://doi.org/10.1016/j.neunet.2019.04.008 doi: 10.1016/j.neunet.2019.04.008
[8]	S. Yang, Z. Guo, J. Wang, Robust synchronization of multiple memristive neural networks with uncertain parameters via nonlinear coupling, IEEE T. Syst. Man Cy.-S., 45 (2015), 1077–1086. https://doi.org/10.1109/TSMC.2014.2388199 doi: 10.1109/TSMC.2014.2388199
[9]	H. B. Bao, J. D. Cao, Projective synchronization of fractional-order memristor-based neural networks, Neural Networks, 63 (2015), 1–9. https://doi.org/10.1016/j.neunet.2014.10.007 doi: 10.1016/j.neunet.2014.10.007
[10]	H. Ren, Z. Peng, Y. Gu, Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control, Neural Networks, 130 (2020), 165–175. https://doi.org/10.1016/j.neunet.2020.07.002 doi: 10.1016/j.neunet.2020.07.002
[11]	B. Zhang, F. Deng, S. Xie, S. Luo, Exponential synchronization of stochastic time-delayed memristor-based neural networks via distributed impulsive control, Neurocomputing, 286 (2018), 41–50. https://doi.org/10.1016/j.neucom.2018.01.051 doi: 10.1016/j.neucom.2018.01.051
[12]	R. Rakkiyappan, G. Velmurugan, J. Cao, Stability analysis of memristor-based fractional-order neural networks with different memductance functions, Cogn. Neurodynamics, 9 (2015), 145–177. https://doi.org/10.1007/s11571-014-9312-2 doi: 10.1007/s11571-014-9312-2
[13]	L. Wang, H. He, Z. Zeng, Global synchronization of fuzzy memristive neural networks with discrete and distributed delays, IEEE T. Fuzzy Syst., 28 (2019), 2022–2034. https://doi.org/10.1109/TFUZZ.2019.2930032 doi: 10.1109/TFUZZ.2019.2930032
[14]	J. Chen, Z. Zeng, P. Jiang, Global mittag-leffler stability and synchronization of memristor-based fractional-order neural networks, Neural Networks, 51 (2014), 1–8. https://doi.org/10.1016/j.neunet.2013.11.016 doi: 10.1016/j.neunet.2013.11.016
[15]	S. Liu, Y. Yu, S. Zhang, Robust synchronization of memristor-based fractional-order hopfield neural networks with parameter uncertainties, Neural Comput. Appl., 31 (2019), 3533–3542. https://doi.org/10.1007/s00521-017-3274-3 doi: 10.1007/s00521-017-3274-3
[16]	L. Chen, T. Huang, J. T. Machado, A. M. Lopes, Y. Chai, R. Wu, Delay-dependent criterion for asymptotic stability of a class of fractional-order memristive neural networks with time-varying delays, Neural Networks, 118 (2019), 289–299. https://doi.org/10.1016/j.neunet.2019.07.006 doi: 10.1016/j.neunet.2019.07.006
[17]	H. Cheng, S. Zhong, Q. Zhong, K. Shi, X. Wang, Lag exponential synchronization of delayed memristor-based neural networks via robust analysis, IEEE Access, 7 (2018), 173–182. https://doi.org/10.1109/ACCESS.2018.2885221 doi: 10.1109/ACCESS.2018.2885221
[18]	L. Wang, Z. Zeng, M. F. Ge, A disturbance rejection framework for finite-time and fixed-time stabilization of delayed memristive neural networks, IEEE T. Syst. Man. Cy.-S., 51 (2019), 905–915. https://doi.org/10.1109/TSMC.2018.2888867 doi: 10.1109/TSMC.2018.2888867
[19]	S. Shah, J. Wiener, Advanced differential equations with piecewise constant argument deviations, Int. J. Math. Math. Sci., 6 (1983), 671–703. https://doi.org/10.1155/S0161171283000599 doi: 10.1155/S0161171283000599
[20]	M. U. Akhmet, D. Aruğaslan, E. Yılmaz, Stability analysis of recurrent neural networks with piecewise constant argument of generalized type, Neural Networks, 23 (2010), 805–811. https://doi.org/10.1016/j.neunet.2010.05.006 doi: 10.1016/j.neunet.2010.05.006
[21]	A. Wu, L. Liu, T. Huang, Z. Zeng, Mittag-leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments, Neural Networks, 85 (2017), 118–127. https://doi.org/10.1016/j.neunet.2016.10.002 doi: 10.1016/j.neunet.2016.10.002
[22]	J. E. Zhang, Robustness analysis of global exponential stability of nonlinear systems with deviating argument and stochastic disturbance, IEEE Access, 5 (2017), 446–454. https://doi.org/10.1109/ACCESS.2017.2727500 doi: 10.1109/ACCESS.2017.2727500
[23]	W. X. Fang, T. Xie, B. W. Li, Robustness analysis of fuzzy cellular neural network with deviating argument and stochastic disturbances, IEEE Access, 11 (2023), 2023. https://doi.org/10.1109/ACCESS.2023.3233946 doi: 10.1109/ACCESS.2023.3233946
[24]	G. Bao, S. Wen, Z. Zeng, Robust stability analysis of interval fuzzy cohen-grossberg neural networks with piecewise constant argument of generalized type, Neural Networks, 33 (2012), 32–41. https://doi.org/10.1016/j.neunet.2012.04.003 doi: 10.1016/j.neunet.2012.04.003
[25]	Q. Xi, X. Liu, Finite-time stability and controller design for a class of hybrid dynamical systems with deviating argument, Nonlineat Anal.-Hybri., 39 (2021), 2021. https://doi.org/10.1016/j.nahs.2020.100952 doi: 10.1016/j.nahs.2020.100952
[26]	M. U. Akhmet, D. Aruğaslan, E. Yılmaz, Method of lyapunov functions for differential equations with piecewise constant delay, J. Comput. Appl. Math., 235 (2011), 4554–4560. https://doi.org/10.1016/j.cam.2010.02.043 doi: 10.1016/j.cam.2010.02.043
[27]	W. Fang, T. Xie, B. Li, Robustness analysis of fuzzy bam cellular neural network with time-varying delays and stochastic disturbances, AIMS Math., 8 (2023), 9365–9384. https://doi.org/10.3934/math.2023471 doi: 10.3934/math.2023471
[28]	Q. Zhu, T. Huang, Stability analysis for a class of stochastic delay nonlinear systems driven by g-brownian motion, Syst. Control. Lett., 140 (2020), 104699. https://doi.org/10.1016/j.sysconle.2020.104699 doi: 10.1016/j.sysconle.2020.104699
[29]	Q. Zhu, Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control, IEEE T. Automat. Contr., 64 (2018), 3764–3771. https://doi.org/10.1109/TAC.2018.2882067 doi: 10.1109/TAC.2018.2882067
[30]	L. Zhang, X. Yang, C. Xu, J. Feng, Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control, Appl. Math. Comput., 306 (2017), 22–30. https://doi.org/10.1016/j.amc.2017.02.004 doi: 10.1016/j.amc.2017.02.004
[31]	C. Chen, L. Li, H. Peng, Y. Yang, T. Li, Synchronization control of coupled memristor-based neural networks with mixed delays and stochastic perturbations, Neural Process. Lett., 47 (2018), 679–696. https://doi.org/10.1007/s11063-017-9675-6 doi: 10.1007/s11063-017-9675-6
[32]	X. Wang, K. She, S. Zhong, J. Cheng, Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation, Neurocomputing, 242 (2017), 131–139. https://doi.org/10.1016/j.neucom.2017.02.059 doi: 10.1016/j.neucom.2017.02.059
[33]	Y. Shen, J. Wang, Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances, IEEE T. Neural Net. Learn, 23 (2011), 87–96. https://doi.org/10.1109/TNNLS.2011.2178326 doi: 10.1109/TNNLS.2011.2178326
[34]	Y. Shen, J. Wang, Robustness of global exponential stability of nonlinear systems with random disturbances and time delays, IEEE T. Syst. Man Cy.-S., 46 (2015), 1157–1166. https://doi.org/10.1109/TSMC.2015.2497208 doi: 10.1109/TSMC.2015.2497208
[35]	X. Mao, Stochastic differential equations and applications, Elsevier, 2007.
[36]	Y. Zhang, L. Li, H. Peng, J. Xiao, Y. Yang, M. Zheng, et al., Finite-time synchronization for memristor-based bam neural networks with stochastic perturbations and time-varying delays, Int. J. Robust Nonlin., 28 (2018), 5118–5139. https://doi.org/10.1002/rnc.4302 doi: 10.1002/rnc.4302
[37]	C. Li, J. Lian, Y. Wang, Stability of switched memristive neural networks with impulse and stochastic disturbance, Neurocomputing, 275 (2018), 2565–2573. https://doi.org/10.1016/j.neucom.2017.11.031 doi: 10.1016/j.neucom.2017.11.031
[38]	J. P. Aubin, A. Cellina, Differential inclusions: Set-valued maps and viability theory, Springer Science & Business Media, 2012. https://doi.org/10.1007/978-3-642-69512-4
[39]	X. Mao, Stability and stabilisation of stochastic differential delay equations, IET Control Theory A., 1 (2007), 1551–1566. http://dx.doi.org/10.1049/iet-cta:20070006 doi: 10.1049/iet-cta:20070006
[40]	R. Bellman, The stability of solutions of linear differential equations, Duke Math. J., 10 (1943), 643–647.

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