Skip to main content
SpringerLink
Log in

Fixed-Time Synchronization of Multi-weighted Complex Networks Via Economical Controllers

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper considers the fixed-time synchronization of multi-weighted complex networks (MWCNs) with /without coupling delays. Firstly, the problems of fixed-time average synchronization are solved for the MWCNs model without delays. A corresponding synchronization criterion is proposed as well. Secondly, the issues of fixed-time tracking synchronization of MWCNs with coupling delays are discussed. Some sufficient conditions are given to ensure the considered system achieve the synchronization goal. Thirdly, in contrast to the traditional fixed-time synchronization strategies containing many nonlinear control terms (Hu et al. in Neural Netw 89:74–83, 2017; Chen et al. in Neural Netw 123:412–419, 2020; Yang et al. in IEEE Trans Autom Control 62(11):5511–5521, 2017; Zhang et al. in IEEE Trans Cybern 49(8):3099–3104, 2018; Xu et al. in J Franklin Inst 355(1):164–176, 2018; Liu et al. in IEEE Trans Cybern 49(6):2398–2403, 2018), the new designed control protocols only contain fewer terms, which are economical just as claimed in Li et al. (IEEE Trans Cybern, 2020). Finally, two numerical examples are provided to show the effectiveness of proposed design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Li R, Gao X, Cao J (2019) Exponential synchronization of stochastic memristive neural networks with time-varying delays. Neural Process Lett 49(1):79–102

    Google Scholar 

  2. Yu F, Qian S, Chen X, Huang Y, Liu L, Shi C, Cai S, Song Y, Wang C (2020) A new 4D four-wing memristive hyperchaotic system: dynamical analysis, electronic circuit design, shape synchronization and secure communication. Int J Bifurcat Chaos 30(10):2050147

    MathSciNet  MATH  Google Scholar 

  3. Yu F, Liu L, Shen H, Zhang Z, Huang Y, Shi C, Cai S, Wu X, Du S, Wan Q (2020) Dynamic analysis, circuit design, and synchronization of a novel 6D memristive four-wing hyperchaotic system with multiple coexisting attractors. Complexity. https://doi.org/10.1155/2020/5904607

  4. Huang C, Liu B, Tian X, Yang L, Zhang X (2019) Global convergence on asymptotically almost periodic SICNNs with nonlinear decay functions. Neural Process Lett 49(2):625–641

    Google Scholar 

  5. Liu M, Jiang H, Hu C (2019) New results for exponential synchronization of memristive Cohen-Grossberg neural networks with time-varying delays. Neural Process Lett 49(1):79–102

    Google Scholar 

  6. Huang C, Liu B, Qian C, Cao J (2021) Stability on positive pseudo almost periodic solutions of HPDCNNs incorporating D operator. Math Comput Simul 190:1150–1163

    MathSciNet  MATH  Google Scholar 

  7. Yang X, Liu Y, Rutkowski L (2020) Synchronization of coupled time-delay neural networks with mode-dependent average dwell time switching. IEEE Trans Neural Netw Learn Syst 31(12):5483–5496

    MathSciNet  Google Scholar 

  8. Wang J, Qin Z, Wu H, Huang T (2019) Passivity and synchronization of coupled uncertain reaction-diffusion neural networks with multiple time delays. IEEE Trans Neural Netw Learn Syst 30(8):2434–2448

    MathSciNet  Google Scholar 

  9. Pratap A, Raja R, Alzabut J, Cao J, Rajchakit G, Huang C (2020) Mittag-Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field. Math Methods Appl Sci 43(10):6223–6253

    MathSciNet  MATH  Google Scholar 

  10. Wang J, Wang D, Wu H, Huang T (2021) Output synchronization of complex dynamical networks with multiple output or output derivative couplings. IEEE Trans Cybern 51(2):927–937

    Google Scholar 

  11. Du H, He Y, Cheng Y (2014) Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circuits Syst I 61(6):1778–1788

    Google Scholar 

  12. Liu X, Cao J, Yu W, Song Q (2015) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern 46(10):2360–2371

    Google Scholar 

  13. Bhat SP, Bernstein DS (2000) Finite-time stability of continuous autonomous systems. SIAM J Control Optim 38(3):751–766

    MathSciNet  MATH  Google Scholar 

  14. Mei J, Jiang M, Wang X, Han J, Wang S (2014) Finite-time synchronization of drive-response systems via periodically intermittent adaptive control. J Franklin Inst 351(5):2691–2710

    MathSciNet  MATH  Google Scholar 

  15. Pratap A, Raja R, Cao J, Alzabut J, Huang C (2020) Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks. Adv Differ Equ 1:1–24

    MathSciNet  MATH  Google Scholar 

  16. Xu Y, Zhou W, Xie C, Tong D (2016) Finite-time synchronization of the complex dynamical network with non-derivative and derivative coupling. Neurocomputing 173:1356–1361

    Google Scholar 

  17. Xiao Q, Zeng Z (2017) Scale-limited Lagrange stability and finite-time synchronization for memristive recurrent neural networks on time scales. IEEE Trans Cybern 47(10):2984–2994

    Google Scholar 

  18. Zhou Y, Wan X, Huang C, Yang X (2020) Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control. Appl Math Comput 376:125157

    MathSciNet  MATH  Google Scholar 

  19. Xu C, Yang X, Lu J, Feng J, Alsaadi FE, Hayat T (2018) Finite-time synchronization of networks via quantized intermittent pinning control. IEEE Trans Cybern 48(10):3021–3027

    Google Scholar 

  20. Wu H, Wang X, Liu X, Cao J (2020) Finite/fixed-time bipartite synchronization of coupled delayed neural networks under a unified discontinuous controller. Neural Process Lett 52(2):1359–1376

    Google Scholar 

  21. He H, Liu X, Cao J, Jiang N (2021) Finite/fixed-time synchronization of delayed inertial memristive neural networks with discontinuous activations and disturbances. Neural Process Lett. https://doi.org/10.1007/s11063-021-10552-4

  22. Wang L, Dong T, Ge M (2019) Finite-time synchronization of memristor chaotic systems and its application in image encryption. Appl Math Comput 347:293–305

    MATH  Google Scholar 

  23. Polyakov A (2011) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110

    MathSciNet  MATH  Google Scholar 

  24. Lu W, Liu X, Chen T (2016) A note on finite-time and fixed-time stability. Neural Netw 81:11–15

    MATH  Google Scholar 

  25. Liu X, Chen T (2016) Finite-time and fixed-time cluster synchronization with or without pinning control. IEEE Trans Cybern 48(1):240–252

    Google Scholar 

  26. Liu X, Ho DWC, Song Q, Cao J (2017) Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances. Nonlinear Dyn 90(3):2057–2068

    MathSciNet  MATH  Google Scholar 

  27. Hu C, Yu J, Chen Z, Jiang H, Huang T (2017) Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks. Neural Netw 89:74–83

    MATH  Google Scholar 

  28. Chen C, Li L, Peng H, Yang Y, Mi L, Zhao H (2020) A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. Neural Netw 123:412–419

    MATH  Google Scholar 

  29. Yang X, Lam J, Ho DWC, Feng Z (2017) Fixed-time synchronization of complex networks with impulsive effects via nonchattering control. IEEE Trans Autom Control 62(11):5511–5521

    MathSciNet  MATH  Google Scholar 

  30. Zhang W, Yang X, Li C (2018) Fixed-time stochastic synchronization of complex networks via continuous control. IEEE Trans Cybern 49(8):3099–3104

    Google Scholar 

  31. Chen D, Zhang W, Cao J, Huang C (2020) Fixed time synchronization of delayed quaternion-valued memristor-based neural networks. Adv Differ Equ 1:1–16

    MathSciNet  MATH  Google Scholar 

  32. Xu Y, Meng D, Xie C, You G, Zhou W (2018) A class of fast fixed-time synchronization control for the delayed neural network. J Franklin Inst 355(1):164–176

    MathSciNet  MATH  Google Scholar 

  33. Liu X, Ho DWC, Song Q, Xu W (2018) Finite/fixed-time pinning synchronization of complex networks with stochastic disturbances. IEEE Trans Cybern 49(6):2398–2403

    Google Scholar 

  34. Li N, Wu X, Feng J, Lü J (2020) Fixed-time synchronization of complex dynamical networks: a novel and economical mechanism. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3026996

  35. Du H, Wen G, Wu D, Cheng Y, Lü J (2020) Distributed fixed-time consensus for nonlinear heterogeneous multi-agent systems. Automatica 113:108797

    MathSciNet  MATH  Google Scholar 

  36. Li N, Wu X, Feng J, Xu Y, Lü J (2020) Fixed-time synchronization of coupled neural networks with discontinuous activation and mismatched parameters. IEEE Trans Neural Netw Learn Syst 32(6):2470–2482

    MathSciNet  Google Scholar 

  37. Qin Z, Wang J, Huang Y, Ren S (2017) Synchronization and \(H_\infty \) synchronization of multi-weighted complex delayed dynamical networks with fixed and switching topologies. J Franklin Inst 354(15):7119–7138

    MathSciNet  MATH  Google Scholar 

  38. Yi C, Feng J, Wang J, Xu C, Zhao Y, Gu Y (2019) Pinning synchronization of nonlinear and delayed coupled neural networks with multi-weights via aperiodically intermittent control. Neural Process Lett 49(1):141–157

    Google Scholar 

  39. Hou J, Huang Y, Ren S (2019) Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms. Neurocomputing 330:78–93

    Google Scholar 

  40. Xu Y, Wu X, Mao B, Lu J, Xie C (2021) Finite-time intra-layer and inter-layer quasi-synchronization of two-layer multi-weighted networks. IEEE Trans Circuits Syst I 68(4):1589–1598

    MathSciNet  Google Scholar 

  41. Qiu S, Huang Y, Ren S (2018) Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay. Neurocomputing 275:1250–1260

    Google Scholar 

  42. Hou J, Huang Y, Yang E (2019) Finite-time anti-synchronization of multi-weighted coupled neural networks with and without coupling delays. Neural Process Lett 50(3):2871–2898

    Google Scholar 

  43. Tan F, Zhou L, Chu Y, Li Y (2020) Fixed-time stochastic outer synchronization in double-layered multi-weighted coupling networks with adaptive chattering-free control. Neurocomputing 399:8–17

    Google Scholar 

  44. Lu W, Chen T (2006) New approach to synchronization analysis of linearly coupled ordinary differential systems. Phys D 213:214–230

    MathSciNet  MATH  Google Scholar 

  45. Hardy GH, Littlewood JE, Pólya G, Littlewood DE (1952) Inequalities. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  46. Hu T, Mohammad K, Mokhtar M, Gholam P, Sarkhel HT, Tarik AR (2021) Real-time COVID-19 diagnosis from X-Ray images using deep CNN and extreme learning machines stabilized by chimp optimization algorithm. Biomed Signal Process Control 68:102764

    Google Scholar 

  47. Wu C, Mohammad K, Mokhtar M, Sarkhel H. T, Tarik A. R, (2021) Evolving deep convolutional neutral network by hybrid sine-cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images. Soft Comput. https://doi.org/10.1007/s00500-021-05839-6

  48. Khishe M, Mosavi MR (2020) Classification of underwater acoustical dataset using neural network trained by chimp optimization algorithm. Appl Acoust 157:107005

    Google Scholar 

  49. Mohammad K, Abbas S (2019) Classification of sonar targets using an MLP neural network trained by dragonfly algorithm. Wirel Personal Commun 108:2241–2260

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant No. 61773185, and in part by Qing Lan Project.

Author information

Authors and Affiliations

  1. Research Center for Complex Networks and Swarm Intelligence, School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, China

    Xiaoyang Liu, Shao Shao & Yuanfa Hu

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

Authors
  1. Xiaoyang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shao Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuanfa Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinde Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyang Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Shao, S., Hu, Y. et al. Fixed-Time Synchronization of Multi-weighted Complex Networks Via Economical Controllers. Neural Process Lett 54, 5023–5041 (2022). https://doi.org/10.1007/s11063-022-10846-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10846-1

Keywords

Search

Navigation