Hybrid impulsive synchronization control of heterogeneous neural networks under dynamic and static event-triggered conditions

Chengyi Jia; Sijiao Sun; Fang Han; Xiaoyan Liu; Chengyi Jia; Sijiao Sun; Fang Han; Xiaoyan Liu

doi:10.3934/era.2026121

Electronic Research Archive

2026, Volume 34, Issue 4: 2607-2630. doi: 10.3934/era.2026121

Previous Article Next Article

Research article Special Issues

Hybrid impulsive synchronization control of heterogeneous neural networks under dynamic and static event-triggered conditions

1.
School of Information and Intelligent Sciences, Donghua University, Shanghai 201620, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Received: 26 January 2026 Revised: 14 March 2026 Accepted: 17 March 2026 Published: 25 March 2026

To address the synchronization control problem of heterogeneous neural networks, this paper proposed a novel adaptive impulsive hybrid control strategy incorporating state feedback and event-triggered mechanisms. First, based on Lyapunov stability theory, the effectiveness of the designed controller was established under a static event-triggered scheme, achieving synchronization of heterogeneous neural networks while avoiding Zeno behavior. Then, an auxiliary parameter was introduced to dynamically adjust the triggering threshold, thereby constructing a dynamic event-triggered mechanism. On the basis of the static triggering principle, the validity of the controller under the dynamic event-triggered condition was further verified. Finally, numerical simulations were conducted to demonstrate the effectiveness and feasibility of the proposed method. The results show that, compared with the traditional static triggering strategy, the dynamic event-triggered scheme can guarantee synchronization performance while significantly reducing the number of triggering events and lowering system resource consumption, thereby validating the advantages of the proposed approach.
- heterogeneous neural networks,
- impulsive control,
- dynamic event-triggered mechanism,
- Zeno behavior,
- synchronization
Citation: Chengyi Jia, Sijiao Sun, Fang Han, Xiaoyan Liu. Hybrid impulsive synchronization control of heterogeneous neural networks under dynamic and static event-triggered conditions[J]. Electronic Research Archive, 2026, 34(4): 2607-2630. doi: 10.3934/era.2026121

Related Papers:

Abstract

To address the synchronization control problem of heterogeneous neural networks, this paper proposed a novel adaptive impulsive hybrid control strategy incorporating state feedback and event-triggered mechanisms. First, based on Lyapunov stability theory, the effectiveness of the designed controller was established under a static event-triggered scheme, achieving synchronization of heterogeneous neural networks while avoiding Zeno behavior. Then, an auxiliary parameter was introduced to dynamically adjust the triggering threshold, thereby constructing a dynamic event-triggered mechanism. On the basis of the static triggering principle, the validity of the controller under the dynamic event-triggered condition was further verified. Finally, numerical simulations were conducted to demonstrate the effectiveness and feasibility of the proposed method. The results show that, compared with the traditional static triggering strategy, the dynamic event-triggered scheme can guarantee synchronization performance while significantly reducing the number of triggering events and lowering system resource consumption, thereby validating the advantages of the proposed approach.

References

[1]	Z. D. Wang, Y. R. Liu, M. Z. Li, X. H. Liu, Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays, IEEE Trans. Neural Networks, 17 (2006), 814–820. https://doi.org/10.1109/TNN.2006.872355 doi: 10.1109/TNN.2006.872355
[2]	J. H. Li, H. L. Dong, Z. D. Wang, X. Y. Bu, Partial-neurons-based passivity-guaranteed state estimation for neural networks with randomly occurring time delays, IEEE Trans. Neural Networks Learn. Syst., 31 (2020), 3747–3753. https://doi.org/10.1109/tnnls.2019.2944552 doi: 10.1109/tnnls.2019.2944552
[3]	A. I. Luppi, F. E. Rosas, P. A. M. Mediano, D. K. Menon, E. A. Stamatakis, Information decomposition and the informational architecture of the brain, Trends Cognit. Sci., 28 (2024), 352–368. https://doi.org/10.1016/j.tics.2023.11.005 doi: 10.1016/j.tics.2023.11.005
[4]	T. Chen, L. Zhu, C. Deng, R. Cao, Y. Wang, S. Zhang, Sam-adapter: adapting segment anything in underperformed scenes, in 2023 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW), (2023), 3359–3367. https://doi.org/10.1109/ICCVW60793.2023.00361
[5]	X. Fu, S. Zhang, T. Chen, Y. Lu, L. Zhu, X. Zhou, Panoptic NeRF: 3D-to-2D label transfer for panoptic urban scene segmentation, in 2022 International Conference on 3D Vision (3DV), (2022), 1–11. https://doi.org/10.1109/3DV57658.2022.00042
[6]	T. Wu, S. He, J. Liu, S. Sun, K. Liu, Q. Han, A brief overview of ChatGPT: the history, status quo and potential future development, IEEE/CAA J. Autom. Sin., 10 (2023), 1122–1136. https://doi.org/10.1109/jas.2023.123618 doi: 10.1109/jas.2023.123618
[7]	L. Ding, Q. Han, X. Ge, X. Zhang, An overview of recent advances in event-triggered consensus of multiagent systems, IEEE Trans. Cybern., 48 (2017), 1110–1123. https://doi.org/10.1109/tcyb.2017.2771560 doi: 10.1109/tcyb.2017.2771560
[8]	X. M. Zhang, Q. L. Han, X. Ge, D. Ding, L. Ding, D. Yue, Networked control systems: a survey of trends and techniques, IEEE/CAA J. Autom. Sin., 7 (2019), 1–17. https://doi.org/10.1109/jas.2019.1911651 doi: 10.1109/jas.2019.1911651
[9]	X. Ge, Q. Han, L. Ding, Y. Wang, X. Zhang, Dynamic event-triggered distributed coordination control and its applications: a survey of trends and techniques, IEEE Trans. Syst. Man Cybern.: Syst., 50 (2020), 3112–3125. https://doi.org/10.1109/tsmc.2020.3010825 doi: 10.1109/tsmc.2020.3010825
[10]	D. H. Chang, Y. Geng, Distributed data-driven iterative learning control for multi-agent systems with unknown input-output coupled parameters, Electron. Res. Arch., 33 (2025), 867–889. https://doi.org/10.3934/era.2025039 doi: 10.3934/era.2025039
[11]	Y. Gong, Consensus control of multi-agent systems with delays, Electron. Res. Arch., 32 (2024), 4887–4904. https://doi.org/10.3934/era.2024224 doi: 10.3934/era.2024224
[12]	T. M. Priyanka, A. Gowrisankar, Multifractality on chaos and bursting oscillations in 4D heterogeneous Hopfield neural network with a memristor-based adaptive activation function, Neurocomputing, 658 (2025), 131780. https://doi.org/10.1016/j.neucom.2025.131780 doi: 10.1016/j.neucom.2025.131780
[13]	S. Sun, Z. Wang, C. Jin, Y. Feng, M. Xiao, C. Zheng, Event-triggered synchronization of a two-layer heterogeneous neural network via hybrid control, Commun. Nonlinear Sci. Numer. Simul., 123 (2023), 107279. https://doi.org/10.1016/j.cnsns.2023.107279 doi: 10.1016/j.cnsns.2023.107279
[14]	M. Shen, C. Wang, Q. G. Wang, H. Yan, G. Zong, Z. H. Zhu, Fault-tolerant synchronization control of switched complex networks by a proportional–integral intermediate observer approach, IEEE Trans. Cybern., 55 (2025), 4689–4698. https://doi.org/10.1109/TCYB.2025.3591393 doi: 10.1109/TCYB.2025.3591393
[15]	N. Li, J. Cao, New synchronization criteria for memristor-based networks: adaptive control and feedback control schemes, Neural Networks, 61 (2015), 1–9. https://doi.org/10.1016/j.neunet.2014.08.015 doi: 10.1016/j.neunet.2014.08.015
[16]	Z. Yang, B. Luo, D. Liu, Y. Li, Adaptive synchronization of delayed memristive neural networks with unknown parameters, IEEE Trans. Syst. Man Cybern.: Syst., 50 (2017), 539–549. https://doi.org/10.1109/tsmc.2017.2778092 doi: 10.1109/tsmc.2017.2778092
[17]	S. Wen, T. Huang, X. Yu, M. Z. Q. Chen, Z. Zeng, Aperiodic sampled-data sliding-mode control of fuzzy systems with communication delays via the event-triggered method, IEEE Trans. Fuzzy Syst., 24 (2015), 1048–1057. https://doi.org/10.1109/tfuzz.2015.2501412 doi: 10.1109/tfuzz.2015.2501412
[18]	S. Wen, T. Huang, X. Yu, M. Z. Q. Chen, Z. Zeng, Sliding-mode control of memristive Chua's systems via the event-based method, IEEE Trans. Circuits Syst. II Express Briefs, 64 (2016), 81–85. https://doi.org/10.1109/tcsii.2016.2538727 doi: 10.1109/tcsii.2016.2538727
[19]	P. Wang, Q. Zhang, H. Su, Aperiodically intermittent control for synchronization of discrete-time delayed neural networks, J. Franklin Inst., 359 (2022), 4915–4937. https://doi.org/10.1016/j.jfranklin.2022.04.033 doi: 10.1016/j.jfranklin.2022.04.033
[20]	Y. Jiang, S. Luo, Periodically intermittent synchronization of stochastic delayed neural networks, Circuits Syst. Signal Process., 36 (2017), 1426–1444. https://doi.org/10.1007/s00034-016-0377-5 doi: 10.1007/s00034-016-0377-5
[21]	Y. W. Wang, Y. Lei, T. Bian, Z. Guan, Distributed control of nonlinear multiagent systems with unknown and nonidentical control directions via event-triggered communication, IEEE Trans. Cybern., 50 (2019), 1820–1832. https://doi.org/10.1109/TCYB.2019.2908874 doi: 10.1109/TCYB.2019.2908874
[22]	L. Liu, H. Bao, Event-triggered impulsive synchronization of coupled delayed memristive neural networks under dynamic and static conditions, Neurocomputing, 504 (2022), 109–122. https://doi.org/10.1016/j.neucom.2022.06.098 doi: 10.1016/j.neucom.2022.06.098
[23]	Y. Zhou, Z. Zeng, Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays, Neural Networks, 110 (2019), 55–65. https://doi.org/10.1016/j.neunet.2018.09.014 doi: 10.1016/j.neunet.2018.09.014
[24]	Y. Zhou, H. Zhang, Z. Zeng, Quasisynchronization of memristive neural networks with communication delays via event-triggered impulsive control, IEEE Trans. Cybern., 52 (2020), 7682–7693. https://doi.org/10.1109/tcyb.2020.3035358 doi: 10.1109/tcyb.2020.3035358
[25]	A. Kazemy, J. Lam, X. M. Zhang, Event-triggered output feedback synchronization of master–slave neural networks under deception attacks, IEEE Trans. Neural Networks Learn. Syst., 33 (2020), 952–961. https://doi.org/10.1109/TNNLS.2020.3030638 doi: 10.1109/TNNLS.2020.3030638
[26]	Y. Zhou, H. Zhang, Z. Zeng, Synchronization of memristive neural networks with unknown parameters via event-triggered adaptive control, Neural Networks, 139 (2021), 255–264. https://doi.org/10.1016/j.neunet.2021.02.029 doi: 10.1016/j.neunet.2021.02.029
[27]	W. He, B. Xu, Q. L. Han, F. Qian, Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies, IEEE Trans. Cybern., 50 (2019), 2996–3008. https://doi.org/10.1109/tcyb.2019.2920093 doi: 10.1109/tcyb.2019.2920093
[28]	H. Zhang, T. Ma, G. B. Huang, Z. Wang, Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control, IEEE Trans. Syst. Man Cybern. Part B Cybern., 40 (2009), 831–844. https://doi.org/10.1109/tsmcb.2009.2030506 doi: 10.1109/tsmcb.2009.2030506
[29]	Z. Tang, J. H. Park, J. Feng, Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay, IEEE Trans. Neural Networks Learn. Syst., 29 (2017), 908–919. https://doi.org/10.1109/tnnls.2017.2651024 doi: 10.1109/tnnls.2017.2651024
[30]	W. Zhu, D. Wang, L. Liu, G. Feng, Event-based impulsive control of continuous-time dynamic systems and its application to synchronization of memristive neural networks, IEEE Trans. Neural Networks Learn. Syst., 29 (2017), 3599–3609. https://doi.org/10.1109/tnnls.2017.2731865 doi: 10.1109/tnnls.2017.2731865

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)