Research article

New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks


  • Received: 26 October 2022 Revised: 11 November 2022 Accepted: 22 November 2022 Published: 01 December 2022
  • In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.

    Citation: Zhen Yang, Zhengqiu Zhang, Xiaoli Wang. New finite-time synchronization conditions of delayed multinonidentical coupled complex dynamical networks[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3047-3069. doi: 10.3934/mbe.2023144

    Related Papers:

  • In this article, we mainly focus on the finite-time synchronization of delayed multinonidentical coupled complex dynamical networks. By applying the Zero-point theorem, novel differential inequalities, and designing three novel controllers, we obtain three new criteria to assure the finite-time synchronization between the drive system and the response system. The inequalities occurred in this paper are absolutely different from those in other papers. And the controllers provided here are fully novel. We also illustrate the theoretical results through some examples.



    加载中


    [1] S. Zhu, J. Zhou, X. Yu, J. Lu, Synchronization of complex networks with nondifferentiable time-varying delay, IEEE Trans. Cybern., 52 (2022), 3342–3348. https://doi.org/10.1109/TCYB.2020.3022976 doi: 10.1109/TCYB.2020.3022976
    [2] X. He, H. Zhang, Exponential synchronization of complex networks via feedback control and periodically intermittent noise, J. Franklin Inst., 359 (2022), 3614–3630. https://doi.org/10.1016/j.jfranklin.2022.03.010 doi: 10.1016/j.jfranklin.2022.03.010
    [3] S. Zhu, J. Zhou, Q. Zhu, N. Li, J. Lu, Adaptive exponential synchronization of complex networks with nondifferentiable time-varying delay, IEEE Trans. Neural Networks Learn. Syst., 2022. https://doi.org/10.1109/TNNLS.2022.3145843 doi: 10.1109/TNNLS.2022.3145843
    [4] L. Shi, C. Zhang, S. Zhong, Synchronization of singular complex networks with time-varying delay via pinning control and linear feedback control, Chaos Solitons Fractals, 145 (2021), 110805. https://doi.org/10.1016/j.chaos.2021.110805 doi: 10.1016/j.chaos.2021.110805
    [5] X. Liu, Synchronization and control for multiweighted and directed complex networks, IEEE Trans. Neural Networks Learn. Syst., 2021. https://doi.org/10.1109/TNNLS.2021.3110681 doi: 10.1109/TNNLS.2021.3110681
    [6] J. Wang, J. Xia, H. Shen, M. Xing, J. H. Park, $H_{\infty}$ synchronization for fuzzy markov jump chaotic systems with piecewise-constant transition probabilities subject to PDT switching rule, IEEE Trans. Fuzzy Syst., 29 (2021), 3082–3092. https://doi.org/10.1109/TFUZZ.2020.3012761 doi: 10.1109/TFUZZ.2020.3012761
    [7] Y. Wu, B. Shen, C. K. Ahn, W. Li, Intermittent dynamic event-triggered control for synchronization of stochastic complex networks, IEEE Trans. Circuits Syst. I Regul. Pap., 68 (2021), 2639–2650. https://doi.org/10.1109/TCSI.2021.3071034 doi: 10.1109/TCSI.2021.3071034
    [8] H. Gu, K. Liu, J. L$\ddot{\mathrm{u}}$, Adaptive PI control for synchronization of complex networks with stochastic coupling and nonlinear dynamics, IEEE Trans. Circuits Syst. I Regul. Pap., 67 (2020), 5268–5280. https://doi.org/10.1109/TCSI.2020.3020146 doi: 10.1109/TCSI.2020.3020146
    [9] Y. Liu, Z. Wang, L. Ma, Y. Cui, F. E. Alsaadi, Synchronization of directed switched complex networks with stochastic link perturbations and mixed time-delays, Nonlinear Anal.-Hybrid Syst., 27 (2018), 213–224. https://doi.org/10.1016/j.nahs.2017.07.006 doi: 10.1016/j.nahs.2017.07.006
    [10] 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
    [11] R. Sakthivel, M. Sathishkumar, B. Kaviarasan, S. M. Anthoni, Synchronization and state estimation for stochastic complex networks with uncertain inner coupling, Neurocomputing, 238 (2017), 44–55. https://doi.org/10.1016/j.neucom.2017.01.035 doi: 10.1016/j.neucom.2017.01.035
    [12] A. Hongsri, T. Botmart, W. Weera, P. Junsawang, New delay-dependent synchronization criteria of complex dynamical networks with time-varying coupling delay based on sampled-data control via new integral inequality, IEEE Access, 9 (2021), 64958–64971. https://doi.org/10.1109/ACCESS.2021.3076361 doi: 10.1109/ACCESS.2021.3076361
    [13] X. Yi, L. Ren, Z. Zhang, New criteria on global asymptotic synchronization of Duffing-type oscillator system, Nonlinear Anal. Model. Control, 25 (2020), 378–399. https://doi.org/10.15388/namc.2020.25.16656 doi: 10.15388/namc.2020.25.16656
    [14] D. L$\acute{\mathrm{o}}$pez-Mancilla, G. L$\acute{\mathrm{o}}$pez-Cahuich, C. Posadas-Castillo, C. E. Casta$\tilde{\mathrm{n}}$eda, J. H. Garc$\acute{\mathrm{l}}$a-L$\acute{\mathrm{o}}$pez, J. L. V$\acute{\mathrm{a}}$zquez-Guti$\acute{\mathrm{e}}$rrez, et al., Synchronization of complex networks of identical and nonidentical chaotic systems via modelmatching control, PLoS ONE, 14 (2019), e0216349. https://doi.org/10.1371/journal.pone.0216349 doi: 10.1371/journal.pone.0216349
    [15] K. Sivaranjani, R. Rakkiyappan, J. Cao, A. Alsaedi, Synchronization of nonlinear singularly perturb e d complex networks with uncertain inner coupling via event triggered control, Appl. Math. Comput., 311 (2017), 283–299. https://doi.org/10.1016/j.amc.2017.05.007 doi: 10.1016/j.amc.2017.05.007
    [16] H. Dai, W. Chen, J. Jia, J. Liu, Z. Zhang, Exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication, Neurocomputing, 245 (2017), 124–132. https://doi.org/10.1016/j.neucom.2017.03.035 doi: 10.1016/j.neucom.2017.03.035
    [17] C. Zhang, X. Wang, C. Wang, Synchronization of complex networks with time-varying inner coupling and outer coupling matrices, Math. Methods Appl. Sci., 40 (2017), 4237–4245. https://doi.org/10.1002/mma.4300 doi: 10.1002/mma.4300
    [18] R. Sakthivel, R. Sakthivel, F. Alzahrani, P. Selvaraj, S. M. Anthoni, Synchronization of complex dynamical networks with random coupling delay and actuator faults, ISA Trans., 94 (2019), 57–69. https://doi.org/10.1016/j.isatra.2019.03.029 doi: 10.1016/j.isatra.2019.03.029
    [19] Y. Wu, R. Lu, P. Shi, H. Su, Z. Wu, Sampled-data synchronization of complex networks with partial couplings and T-S fuzzy nodes, IEEE Trans. Fuzzy Syst., 26 (2018), 782–793. https://doi.org/10.1109/TFUZZ.2017.2688490 doi: 10.1109/TFUZZ.2017.2688490
    [20] 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. Cybern., 50 (2020), 4043–4052. https://doi.org/10.1109/TCYB.2019.2938217 doi: 10.1109/TCYB.2019.2938217
    [21] Y. Bao, Y. Zhang, Synchronization of complex networks with memristive neural network nodes via impulsive control, in 2019 Chinese Control And Decision Conference (CCDC), 2019, 2355–2360. https://doi.org/10.1109/CCDC.2019.8833419
    [22] X. Yang, J. Lu, D. W. C. Ho, Q. Song, Synchronization of uncertain hybrid switching and impulsive complex networks, Appl. Math. Model., 59 (2018), 379–392. https://doi.org/10.1016/j.apm.2018.01.046 doi: 10.1016/j.apm.2018.01.046
    [23] X. Yao, Y. Liu, Z. Zhang, W. Wan, Synchronization rather than finite-time synchronization results of fractional-order multi-weighted complex networks, IEEE Trans. Neural Networks Learn. Syst., 2021. https://doi.org/10.1109/TNNLS.2021.3083886 doi: 10.1109/TNNLS.2021.3083886
    [24] V. K. Yadav, V. K. Shukla, S. Das, Exponential synchronization of fractional-order complex chaotic systems and its application, Chaos Solitons Fractals, 147 (2021), 110937. https://doi.org/10.1016/j.chaos.2021.110937 doi: 10.1016/j.chaos.2021.110937
    [25] Y. Yang, C. Hua, J. Yu, H. Jiang, S. Wen, Synchronization of fractional-order spatiotemporal complex networks with boundary communication, Neurocomputing, 450 (2021), 197–207. https://doi.org/10.1016/j.neucom.2021.04.008 doi: 10.1016/j.neucom.2021.04.008
    [26] L. Li, X. Liu, M. Tang, S. Zhang, X. Zhang, Asymptotical synchronization analysis of fractional-order complex neural networks with non-delayed and delayed couplings, Neurocomputing, 445 (2021), 180–193. https://doi.org/10.1016/j.neucom.2021.03.001 doi: 10.1016/j.neucom.2021.03.001
    [27] Y. Xu, Q. Wang, W. Li, J. Feng, Stability and synchronization of fractional-order delayed multilink complex networks with nonlinear hybrid couplings, Math. Methods Appl. Sci., 44 (2021), 3356–3375. https://doi.org/10.1002/mma.6946 doi: 10.1002/mma.6946
    [28] H. Li, J. Cao, C. Hu, L. Zhang, Z. Wang, Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control, Neurocomputing, 356 (2019), 31–39. https://doi.org/10.1016/j.neucom.2019.04.059 doi: 10.1016/j.neucom.2019.04.059
    [29] Z. Hu, H. Ren, P. Shi, Synchronization of complex dynamical networks subject to noisy sampling interval and packet loss, IEEE Trans. Neural Networks Learn. Syst., 33 (2022), 3216–3226. https://doi.org/10.1109/TNNLS.2021.3051052 doi: 10.1109/TNNLS.2021.3051052
    [30] J. Feng, L. Zhang, J. Wang, Y. Zhao, The synchronization of complex dynamical networks with discontinuous dynamics and exogenous disturbances, Asian J. Control, 23 (2021), 2837–2848. https://doi.org/10.1002/asjc.2414 doi: 10.1002/asjc.2414
    [31] B. Reh$\acute{\mathrm{a}}$k, V. Lynnyk, Synchronization of symmetric complex networks with heterogeneous time delays, in 2019 22nd International Conference on Process Control (PC19), 2019, 68–73. https://doi.org/10.1109/PC.2019.8815036
    [32] A. Kazemy, K. Shojaei, Synchronization of complex dynamical networks with dynamical behavior links, Asian J. Control, 22 (2020), 474–485. https://doi.org/10.1002/asjc.1910 doi: 10.1002/asjc.1910
    [33] J. Zhang, J. Sun, Exponential synchronization of complex networks with continuous dynamics and Boolean mechanism, Neurocomputing, 307 (2018), 146–152. https://doi.org/10.1016/j.neucom.2018.03.061 doi: 10.1016/j.neucom.2018.03.061
    [34] M. A. Alamin Ahmeda, Y. Liu, W. Zhang, F. E. Alsaadic, Exponential synchronization via pinning adaptive control for complex networks of networks with time delays, Neurocomputing, 225 (2017), 198–204. https://doi.org/10.1016/j.neucom.2016.11.022 doi: 10.1016/j.neucom.2016.11.022
    [35] Q. Cui, L. Li, J. Lu, A. Alofi, Finite-time synchronization of complex dynamical networks under delayed impulsive effects, Appl. Math. Comput., 430 (2022), 127290. https://doi.org/10.1016/j.amc.2022.127290 doi: 10.1016/j.amc.2022.127290
    [36] H. Zhang, X. Zheng, N. Li, Finite-Time pinning synchronization control for coupled complex networks with time-varying delays, Discrete Dyn. Nat. Soc., 2022 (2022), 7119370. https://doi.org/10.1155/2022/7119370 doi: 10.1155/2022/7119370
    [37] J. Wang, L. Zhao, H. Wu, T. Huang, Finite-time passivity and synchronization of multi-weighted complex dynamical networks under PD control, IEEE Trans. Neural Networks Learn. Syst., 2022. Available from: https://doi.org/10.1109/TNNLS.2022.3175747 doi: 10.1109/TNNLS.2022.3175747
    [38] N. Gunasekaran, M. S. Ali, S. Arik, H. I. Abdul Ghaffar, A. A. Zaki Diab, Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal, Neural Networks, 149 (2022), 137–145. https://doi.org/10.1016/j.neunet.2022.02.013 doi: 10.1016/j.neunet.2022.02.013
    [39] W. Yuan, Y. Ma, Finite-time $\mathcal{H}_{\infty}$ synchronization for complex dynamical networks with time-varying delays based on adaptive control, ISA Trans., 128 (2021), 109–122. https://doi.org/10.1016/j.isatra.2021.11.018 doi: 10.1016/j.isatra.2021.11.018
    [40] W. Zhang, X. Yang, S. Yang, A. Alsaedi, Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs, Math. Comput. Simul., 188 (2021), 319–329. https://doi.org/10.1016/j.matcom.2021.04.013 doi: 10.1016/j.matcom.2021.04.013
    [41] M. S. Ali, L. Palanisamy, N. Gunasekaran, A. Alsaedi, B. Ahmad, Finite-time exponential synchronization of reaction-diffusion delayed complex-dynamical networks, Discrete Cont. Dyn.-S, 14 (2021), 1465–1477. https://doi.org/10.3934/dcdss.2020395 doi: 10.3934/dcdss.2020395
    [42] X. Li, H. Wub, J. Cao, Synchronization in finite time for variable-order fractional complex dynamic networks with multi-weights and discontinuous nodes based on sliding mode control strategy, Neural Networks, 139 (2021), 335–347. https://doi.org/10.1016/j.neunet.2021.03.033 doi: 10.1016/j.neunet.2021.03.033
    [43] J. He, H. Chen, M. Ge, T. Ding, L. Wang, C. Liang, Adaptive finite-time quantized synchronization of complex dynamical networks with quantized time-varying delayed couplings, Neurocomputing, 431 (2021), 90–99. https://doi.org/10.1016/j.neucom.2020.12.038 doi: 10.1016/j.neucom.2020.12.038
    [44] Y. Luo, Y. Yao, Z. Cheng, X. Xiao, H. Liu, Event-triggered control for coupled reaction-diffusion complex network systems with finite-time synchronization, Phys. A, 562 (2021), 125219. https://doi.org/10.1016/j.physa.2020.125219 doi: 10.1016/j.physa.2020.125219
    [45] Y. Ren, H. Jiang, J. Li, B. Lu, Finite-time synchronization of stochastic complex networks with random coupling delay via quantized aperiodically intermittent control, Neurocomputing, 420 (2021), 337–348. https://doi.org/10.1016/j.neucom.2020.05.103 doi: 10.1016/j.neucom.2020.05.103
    [46] J. Wang, Z. Qin, H. Wu, T. Huang, Finite-time synchronization and $\mathcal{H}_{\infty}$ synchronization of multiweighted complex networks with adaptive state couplings, IEEE Trans. Cybern., 50 (2020), 600–612. https://doi.org/10.1109/TCYB.2018.2870133 doi: 10.1109/TCYB.2018.2870133
    [47] J. Wang, T. Ru, J. Xia, Y. Wei, Z. Wang, Finite-time synchronization for complex dynamic networks with semi-Markov switching topologies: An $\mathcal{H}_{\infty}$ event-triggered control scheme, Appl. Math. Comput., 356 (2019), 235–251. https://doi.org/10.1016/j.amc.2019.03.037 doi: 10.1016/j.amc.2019.03.037
    [48] H. Li, J. Cao, H. Jiang, A. Alsaedi, Finite-time synchronization and parameter identification of uncertain fractional-order complex networks, Phys. A, 533 (2019), 122027. https://doi.org/10.1016/j.physa.2019.122027 doi: 10.1016/j.physa.2019.122027
    [49] X. Liu, D. W. C. Ho, Q. Song, W. Xu, Finite/Fixed-Time Pinning Synchronization of Complex Networks With Stochastic Disturbances, IEEE Trans. Cybern., 49 (2019), 2398–2403. https://doi.org/10.1109/TCYB.2018.2821119 doi: 10.1109/TCYB.2018.2821119
    [50] W. Jiang, L. Li, Z. Tu, Y. Feng, Semiglobal finite-time synchronization of complex networks with stochastic disturbance via intermittent control, Int. J. Robust Nonlinear Control, 29 (2019), 2351–2363. https://doi.org/10.1002/rnc.4496 doi: 10.1002/rnc.4496
    [51] H. Li, J. Cao, H. Jiang, A. Alsaedi, Finite-time synchronization of fractional-order complex networks via hybrid feedback control, Neurocomputing, 320 (2018), 69–75. https://doi.org/10.1016/j.neucom.2018.09.021 doi: 10.1016/j.neucom.2018.09.021
    [52] G. Ji, C. Hu, J. Yu, H. Jiang, Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design, J. Franklin Inst., 355 (2018), 4665–4685. https://doi.org/10.1016/j.jfranklin.2018.04.026 doi: 10.1016/j.jfranklin.2018.04.026
    [53] D. Zhang, Y. Shen, J. Mei, Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control, Neurocomputing, 225 (2017), 129–138. https://doi.org/10.1016/j.neucom.2016.11.005 doi: 10.1016/j.neucom.2016.11.005
    [54] N. Gunasekaran, M. S. Ali, S. Arik, H. I. Abdul Ghaffar, A. A. Zaki Diab, Finite-time and sampled-data synchronization of complex dynamical networks subject to average dwell-time switching signal, Neural Networks, 149 (2022), 137–145. https://doi.org/10.1016/j.neunet.2022.02.013 doi: 10.1016/j.neunet.2022.02.013
    [55] N. Gunasekaran, G. Zhai, Q. Yu, Sampled-data synchronization of delayed multi-agent networks and its application to coupled circuit, Neurocomputing, 413 (2020), 499–511. https://doi.org/10.1016/j.neucom.2020.05.060 doi: 10.1016/j.neucom.2020.05.060
    [56] M. Thiele, R. Berner, P. A. Tass, E. Sch$\ddot{o}$ll, S. Yanchuk, Asymmetric Adaptivity induces Recurrent Synchronization in Complex Networks, preprint, arXiv: 2112.08697.
    [57] N. Li, X. Wu, J. Feng, J. L$\ddot{u}$, Fixed-Time Synchronization of Complex Dynamical Networks: A Novel and Economical Mechanism, IEEE Trans. Cybern., 8 (2022), 33072–33079. https://doi.org/10.1109/ACCESS.2020.2970789 doi: 10.1109/ACCESS.2020.2970789
    [58] C. Hu, H. He, H. Jiang, Fixed/Preassigned-time synchronization of complex networks via improving fixed-time stability, IEEE Trans. Cybern., 51 (2021), 2882–2892. https://doi.org/10.1109/TCYB.2020.2977934 doi: 10.1109/TCYB.2020.2977934
    [59] H. Shen, X. Hu, J. Wang, J. Cao, W. Qian, Non-Fragile $H_{\infty}$ synchronization for markov jump singularly perturbed coupled neural networks subject to double-layer switching regulation, IEEE Trans. Neural Networks Learn. Syst., 2021. Available from: https://doi.org/10.1109/TNNLS.2021.3107607
    [60] L. Zhang, J. Zhong, J. Lu, Intermittent control for finite-time synchronization of fractional-order complex networks, Neural Networks, 144 (2021), 11–20. https://doi.org/10.1016/j.neunet.2021.08.004 doi: 10.1016/j.neunet.2021.08.004
    [61] Z. Zhang, J. Cao, Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method, IEEE Trans. Neural Networks Learn. Syst., 30 (2019), 1476–1485. https://doi.org/10.1109/TNNLS.2018.2868800 doi: 10.1109/TNNLS.2018.2868800
    [62] Z. Zhang, M. Chen, A. Li, Further study on finite-time synchronization for delayed inertial neural networks via inequality skills, Neurocomputing, 373 (2020), 15–23. https://doi.org/10.1016/j.neucom.2019.09.034 doi: 10.1016/j.neucom.2019.09.034
    [63] Z. Zhang, J. Cao, Finite-time synchronization for fuzzy inertial neural networks by maximum-value approach, IEEE Trans. Fuzzy Syst., 30 (2022), 1436–1446. https://doi.org/10.1109/TFUZZ.2021.3059953 doi: 10.1109/TFUZZ.2021.3059953
    [64] L. Wang, T. Chen, Finite-time anti-synchronization of neural networks with time-varying delays, Neurocomputing, 275 (2018), 1595–1600. https://doi.org/10.1016/j.neucom.2017.09.097 doi: 10.1016/j.neucom.2017.09.097
    [65] Z. Zhang, T. Zheng, S. Yu, Finite-time anti-synchronization of neural networks with time-varying delays via inequality skills, Neurocomputing, 356 (2019), 60–68. https://doi.org/10.1016/j.neucom.2019.05.012 doi: 10.1016/j.neucom.2019.05.012
    [66] Z. Zhang, A. Li, S. Yu, Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method, Neurocomputing, 318 (2018), 248–260. https://doi.org/10.1016/j.neucom.2018.08.063 doi: 10.1016/j.neucom.2018.08.063
  • Reader Comments
  • © 2023 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1319) PDF downloads(99) Cited by(3)

Article outline

Figures and Tables

Figures(9)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog