Prescribed-time synchronization of inertial memristive neural networks with time-varying delays

Yi Zhu; Minghui Jiang; Yi Zhu; Minghui Jiang

doi:10.3934/math.2025453

AIMS Mathematics

2025, Volume 10, Issue 4: 9900-9916. doi: 10.3934/math.2025453

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Research article

Prescribed-time synchronization of inertial memristive neural networks with time-varying delays

Yi Zhu ^1,2,
Minghui Jiang ^{1,2
,
,}

1.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, Hubei, China
2.
College of Science, China Three Gorges University, Yichang 443002, Hubei, China

Received: 03 March 2025 Revised: 16 April 2025 Accepted: 18 April 2025 Published: 27 April 2025
MSC : 34K35, 92B20, 93D40

This study focused on the prescribed-time synchronization of inertial memristive neural networks (IMNNs) with time-varying delays. Based on existing prescribed-time control theory, a prescribed-time feedback controller suitable for IMNNs was designed by means of a time-varying scaling function. Moreover, the sufficient criteria for the prescribed-time synchronization (PTS) of IMNNs was derived using the non-reduced order method and the prescribed-time stability lemma. The effectiveness of our theoretical results was conclusively demonstrated through a numerical simulation.
- prescribed-time synchronization,
- inertial memristive neural networks,
- time-varying delay,
- non-reduced order method
Citation: Yi Zhu, Minghui Jiang. Prescribed-time synchronization of inertial memristive neural networks with time-varying delays[J]. AIMS Mathematics, 2025, 10(4): 9900-9916. doi: 10.3934/math.2025453

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Abstract

This study focused on the prescribed-time synchronization of inertial memristive neural networks (IMNNs) with time-varying delays. Based on existing prescribed-time control theory, a prescribed-time feedback controller suitable for IMNNs was designed by means of a time-varying scaling function. Moreover, the sufficient criteria for the prescribed-time synchronization (PTS) of IMNNs was derived using the non-reduced order method and the prescribed-time stability lemma. The effectiveness of our theoretical results was conclusively demonstrated through a numerical simulation.

References

[1]	L. Chua, Memristor-the missing circuit element, IEEE Transactions on Circuit Theory, 18 (1971), 507–519. https://doi.org/10.1109/TCT.1971.1083337 doi: 10.1109/TCT.1971.1083337
[2]	J. M. Tour, T. He, The fourth element, Nature, 453 (2008), 42–43. https://doi.org/10.1038/453042a doi: 10.1038/453042a
[3]	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
[4]	F. Corinto, M. Forti, Complex dynamics in arrays of memristor oscillators via the flux-charge method, IEEE Trans. Circuits Syst. I, 65 (2018), 1040–1050. https://doi.org/10.1109/TCSI.2017.2759182 doi: 10.1109/TCSI.2017.2759182
[5]	Y. Wang, H. Tuo, H. Lyu, Z. Cheng, Y. Xin, Aperiodic switching event-triggered stabilization of continuous memristive neural networks with interval delays, Neural Networks, 164 (2023), 264–274. https://doi.org/10.1016/j.neunet.2023.04.036 doi: 10.1016/j.neunet.2023.04.036
[6]	Y. Ho, G. M. Huang, P. Li, Dynamical properties and design analysis for nonvolatile memristor memories, IEEE Trans. Circuits Syst. I, 58 (2011), 724–736. https://doi.org/10.1109/TCSI.2010.2078710 doi: 10.1109/TCSI.2010.2078710
[7]	N. Serafino, M. Zaghloul, Review of nanoscale memristor devices as synapses in neuromorphic systems, In: 2013 IEEE 56th International midwest symposium on circuits and systems (MWSCAS), Columbus, OH, USA, 2013,602–603. https://doi.org/10.1109/MWSCAS.2013.6674720
[8]	L. Wang, H. He, Z. Zeng, Global synchronization of fuzzy memristive neural networks with discrete and distributed delays, IEEE Trans. Fuzzy Syst., 28 (2020), 2022–2034. https://doi.org/10.1109/TFUZZ.2019.2930032 doi: 10.1109/TFUZZ.2019.2930032
[9]	D. Lin, X. Chen, G. Yu, Z. Li, Y. Xia, Global exponential synchronization via nonlinear feedback control for delayed inertial memristor-based quaternion-valued neural networks with impulses, Appl. Math. Comput., 401 (2021), 126093. https://doi.org/10.1016/j.amc.2021.126093 doi: 10.1016/j.amc.2021.126093
[10]	H. Liu, L. Ma, Z. Wang, Y. Liu, F. E. Alsaadi, An overview of stability analysis and state estimation for memristive neural networks, Neurocomputing, 391 (2020), 1–12. https://doi.org/10.1016/j.neucom.2020.01.066 doi: 10.1016/j.neucom.2020.01.066
[11]	Q. Gan, L. Li, J. Yang, Y. Qin, M. Meng, Improved results on fixed-/preassigned-time synchronization for memristive complex-valued neural networks, IEEE Trans. Neur. Netw. Learn. Syst., 33 (2022), 5542–5556. https://doi.org/10.1109/TNNLS.2021.3070966 doi: 10.1109/TNNLS.2021.3070966
[12]	Q. Chang, J. H. Park, Y. Yang, F. Wang, Finite-time multiparty synchronization of T-S fuzzy coupled memristive neural networks with optimal event-triggered control, IEEE Trans. Fuzzy Syst., 31 (2023), 2545–2555. https://doi.org/10.1109/TFUZZ.2022.3228335 doi: 10.1109/TFUZZ.2022.3228335
[13]	R. Guo, S. Xu, B. Zhang, Q. Ma, Nonfragile exponential synchronization for delayed fuzzy memristive inertial neural networks via memory sampled-data control, IEEE Trans. Fuzzy Syst., 32 (2024), 3825–3837. https://doi.org/10.1109/TFUZZ.2024.3386215 doi: 10.1109/TFUZZ.2024.3386215
[14]	Z. Tang, R. Zhu, R. Hu, Y. Chen, E. Q. Wu, H. Wang, A multilayer neural network merging image preprocessing and pattern recognition by integrating diffusion and drift memristors, IEEE Trans. Cogn. Dev. Syst., 13 (2021), 645–656. https://doi.org/10.1109/TCDS.2020.3003377 doi: 10.1109/TCDS.2020.3003377
[15]	K. Deng, S. Zhu, G. Bao, J. Fu, Z. Zeng, Multistability of dynamic memristor delayed cellular neural networks with application to associative memories, IEEE Trans. Neur. Netw. Learn. Syst., 34 (2023), 690–702. https://doi.org/10.1109/TNNLS.2021.3099814 doi: 10.1109/TNNLS.2021.3099814
[16]	W. Yao, C. H. Wang, Y. Sun, S. Gong, H. Lin, Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance, Neural Networks, 164 (2023), 67–80. https://doi.org/10.1016/j.neunet.2023.04.024 doi: 10.1016/j.neunet.2023.04.024
[17]	Z. Chen, Q. Zhang, G. Chen, Fixed-time stabilization for a class of stochastic memristive inertial neural networks with time-varying delays, IEEE Access, 12 (2024), 40496–40507. https://doi.org/10.1109/ACCESS.2024.3373704 doi: 10.1109/ACCESS.2024.3373704
[18]	X. Liu, H. He, J. Cao, Event-triggered bipartite synchronization of delayed inertial memristive neural networks with unknown disturbances, IEEE Trans. Control Netw. Syst., 11 (2024), 1408–1419. https://doi.org/10.1109/TCNS.2023.3338256 doi: 10.1109/TCNS.2023.3338256
[19]	K. L. Babcock, R. M. Westervelt, Stability and dynamics of simple electronic neural networks with added inertia, Physica D, 23 (1986), 464–469. https://doi.org/10.1016/0167-2789(86)90152-1 doi: 10.1016/0167-2789(86)90152-1
[20]	D. W. Wheeler, W. C. Schieve, Stability and chaos in an inertial two neuron system, Physica D, 105 (1997), 267–284. https://doi.org/10.1016/S0167-2789(97)00008-0 doi: 10.1016/S0167-2789(97)00008-0
[21]	D. E. Angelaki, M. J. Correia, Models of membrane resonance in Pigeon semicircular canal type Ⅱ hair cells, Biol. Cybern., 65 (1991), 1–10. https://doi.org/10.1007/BF00197284 doi: 10.1007/BF00197284
[22]	A. Mauro, F. Conti, F. Dodge, R. Schor, Subthreshold behavior and phenomenological impedance of the squid giant axon, J. Gen. Physiol., 55 (1970), 497–523. https://doi.org/10.1085/jgp.55.4.497 doi: 10.1085/jgp.55.4.497
[23]	Z. Song, B. Zhen, D. Hu, Multiple bifurcations and coexistence in an inertial two-neuron system with multiple delays, Cogn. Neurodyn., 14 (2020), 359–374. https://doi.org/10.1007/s11571-020-09575-9 doi: 10.1007/s11571-020-09575-9
[24]	H. Achouri, C. Aouiti, Homoclinic and heteroclinic motions of delayed inertial neural networks, Neural Comput. Appl., 33 (2021), 6983–6998. https://doi.org/10.1007/s00521-020-05472-8 doi: 10.1007/s00521-020-05472-8
[25]	S. Gong, S. Yang, Z. Guo, T. Huang, Global exponential synchronization of inertial memristive neural networks with time-varying delay via nonlinear controller, Neural Networks, 102 (2018), 138–148. https://doi.org/10.1016/j.neunet.2018.03.001 doi: 10.1016/j.neunet.2018.03.001
[26]	L. Zhang, R. Wei, J. Cao, X. Ding, Synchronization control of quaternion-valued inertial memristor-based neural networks via adaptive method, Math. Method. Appl. Sci., 47 (2024), 581–599. https://doi.org/10.1002/mma.9670 doi: 10.1002/mma.9670
[27]	G. Zhang, Z. Zeng, J. Hu, New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays, Neural Networks, 97 (2018), 183–191. https://doi.org/10.1016/j.neunet.2017.10.003 doi: 10.1016/j.neunet.2017.10.003
[28]	A. M. Alimi, C. Aouiti, E. A. Assali, Finite-time and fixed-time synchronization of a class of inertial neural networks with multi-proportional delays and its application to secure communication, Neurocomputing, 332 (2019), 29–43. https://doi.org/10.1016/j.neucom.2018.11.020 doi: 10.1016/j.neucom.2018.11.020
[29]	X. Yang, X. Li, J. Lu, Z. Cheng, Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control, IEEE Trans. Cybernetics, 50 (2020), 4043–4052. https://doi.org/10.1109/TCYB.2019.2938217 doi: 10.1109/TCYB.2019.2938217
[30]	X. Ji, J. Lu, B. Jiang, J. Zhong, Network synchronization under distributed delayed impulsive control: average delayed impulsive weight approach, Nonlinear Anal.-Hybri., 44 (2022), 101148. https://doi.org/10.1016/j.nahs.2021.101148 doi: 10.1016/j.nahs.2021.101148
[31]	T. Luo, Q. Wang, Q. Jia, Y. Xu, Asymptotic and finite-time synchronization of fractional-order multiplex networks with time delays by adaptive and impulsive control, Neurocomputing, 493 (2022), 445–461. https://doi.org/10.1016/j.neucom.2021.12.087 doi: 10.1016/j.neucom.2021.12.087
[32]	Q. Hui, W. M. Haddad, S. P. Bhat, Finite-time semistability and consensus for nonlinear dynamical networks, IEEE Trans. Automat. Contr., 53 (2008), 1887–1900. https://doi.org/10.1109/TAC.2008.929392 doi: 10.1109/TAC.2008.929392
[33]	C. Chen, L. Li, H. Peng, Y. Yang, L. Mi, H. Zhao, A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks, Neural Networks, 123 (2020), 412–419. https://doi.org/10.1016/j.neunet.2019.12.028 doi: 10.1016/j.neunet.2019.12.028
[34]	L. Li, Z. Liu, S. Guo, Z. Ma, P. Huang, Adaptive practical predefined-time control for uncertain teleoperation systems with input saturation and output error constraints, IEEE Trans. Ind. Electron., 71 (2024), 1842–1852. https://doi.org/10.1109/TIE.2023.3250752 doi: 10.1109/TIE.2023.3250752
[35]	C. Hua, P. Ning, K. Li, Adaptive prescribed-time control for a class of uncertain nonlinear systems, IEEE Trans. Automat. Contr., 67 (2022), 6159–6166. https://doi.org/10.1109/TAC.2021.3130883 doi: 10.1109/TAC.2021.3130883
[36]	Y. Pan, W. Ji, H.-K. Lam, L. Cao, An improved predefined-time adaptive neural control approach for nonlinear multiagent systems, IEEE Trans. Autom. Sci. Eng., 21 (2024), 6311–6320. https://doi.org/10.1109/TASE.2023.3324397 doi: 10.1109/TASE.2023.3324397
[37]	A. F. Filippov, Differential equations with discontinuous right-hand sides, Dordrecht: Springer, 1988. https://doi.org/10.1007/978-94-015-7793-9
[38]	J.-P. Aubin, A. Cellina, Differential inclusions, Berlin: Springer, 1984. https://doi.org/10.1007/978-3-642-69512-4
[39]	G. Zhang, Z. Zeng, Stabilization of second-order memristive neural networks with mixed time delays via nonreduced order, IEEE Trans. Neur. Netw. Learn. Syst., 31 (2020), 700–706. https://doi.org/10.1109/TNNLS.2019.2910125 doi: 10.1109/TNNLS.2019.2910125
[40]	J. Holloway, M. Krstic, Prescribed-time output feedback for linear systems in controllable canonical form, Automatica, 107 (2019), 77–85. https://doi.org/10.1016/j.automatica.2019.05.027 doi: 10.1016/j.automatica.2019.05.027
[41]	A. Polyakov, D. Efimov, W. Perruquetti, Finite-time and fixed-time stabilization: implicit Lyapunov function approach, Automatica, 51 (2015), 332–340. https://doi.org/10.1016/j.automatica.2014.10.082 doi: 10.1016/j.automatica.2014.10.082
[42]	Y. Wang, Y. Song, D. J. Hill, M. Krstic, Prescribed-time consensus and containment control of networked multiagent systems, IEEE Trans. Cybernetics, 49 (2019), 1138–1147. https://doi.org/10.1109/TCYB.2017.2788874 doi: 10.1109/TCYB.2017.2788874
[43]	A. Abdurahman, H. Jiang, Z. Teng, Finite-time synchronization for memristor-based neural networks with time-varying delays, Neural Networks, 69 (2015), 20–28. https://doi.org/10.1016/j.neunet.2015.04.015 doi: 10.1016/j.neunet.2015.04.015
[44]	W. Tu, J. Dong, Robust sliding mode control for a class of nonlinear systems through dual-layer sliding mode scheme, J. Franklin I., 360 (2023), 10227–10250. https://doi.org/10.1016/j.jfranklin.2023.07.019 doi: 10.1016/j.jfranklin.2023.07.019
[45]	R. Mahemuti, A. Abdurahman, Predefined-time (PDT) synchronization of impulsive fuzzy BAM neural networks with stochastic perturbations, Mathematics, 11 (2023), 1291. https://doi.org/10.3390/math11061291 doi: 10.3390/math11061291
[46]	X. Hu, L. Wang, C.-K. Zhang, X. Wan, Y. He, Fixed-time stabilization of discontinuous spatiotemporal neural networks with time-varying coefficients via aperiodically switching control, Sci. China Inf. Sci., 66 (2023), 152204. https://doi.org/10.1007/s11432-022-3633-9 doi: 10.1007/s11432-022-3633-9
[47]	G. Zhang, J. Cao, New results on fixed/predefined-time synchronization of delayed fuzzy inertial discontinuous neural networks: non-reduced order approach, Appl. Math. Comput., 440 (2023), 127671. https://doi.org/10.1016/j.amc.2022.127671 doi: 10.1016/j.amc.2022.127671
[48]	A.-T. Nguyen, T. Taniguchi, L. Eciolaza, V. Campos, R. Palhares, M. Sugeno, Fuzzy control systems: past, present and future, IEEE Comput. Intell. M., 14 (2019), 56–68. https://doi.org/10.1109/MCI.2018.2881644
[49]	B. Yin, S. Peng, Prescribed-time/fixed-time synchronization of quaternion-valued neural networks: a method without decomposition, Math. Method. Appl. Sci., in press. https://doi.org/10.1002/mma.10788
[50]	P. Liu, J. Yong, J. Sun, Y. Wang, J. Zhao, Prescribed-time cluster synchronization of coupled inertial neural networks: a lifting dimension approach, Neural Comput. Appl., 36 (2024), 13293–13303. https://doi.org/10.1007/s00521-024-09717-8 doi: 10.1007/s00521-024-09717-8
[51]	H. Yan, Y. Qiao, Z. Ren, L. Duan, J. Miao, Quantized control for predefined-time synchronization of inertial memristive neural networks, Neural Comput. Appl., 36 (2024), 6497–6512. https://doi.org/10.1007/s00521-023-09371-6 doi: 10.1007/s00521-023-09371-6
[52]	F. Wei, G. Chen, Z. Zeng, N. Gunasekaran, Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication, Neural Networks, 167 (2023), 168–182. https://doi.org/10.1016/j.neunet.2023.08.015 doi: 10.1016/j.neunet.2023.08.015

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