Skip to main content
SpringerLink
Log in

Exponentially adaptive synchronization of an uncertain delayed dynamical network

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.

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

Similar content being viewed by others

References

  1. S. H. Strogatz, Exploring complex networks, Nature, 2001, 410(6825): 268–276.

    Article  Google Scholar 

  2. R. Albert and A. L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys., 2002, 74(1): 47–97.

    Article  MATH  Google Scholar 

  3. H. Hong, M. Y. Choi, and B. J. Kim, Synchronization on small-world networks, Phys. Rev. E, 2002, 65(5): 26–139.

    Google Scholar 

  4. J. Lü, X. H. Yu, G. Chen, et al., Characterizing the synchronizability of small-world dynamical networks, IEEE Trans. Circ. Syst. I, 2004, 51(4): 787–796.

    Article  Google Scholar 

  5. C.W. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 2006, 51(7): 1207–1210.

    Article  Google Scholar 

  6. Z. Li and G. Chen, Global synchronization and asymptotic stability of complex dynamical networks, IEEE Trans. Circ. Syst. II, 2006, 53(1): 28–33.

    Article  Google Scholar 

  7. J. Lü, X. Yu, and G. Chen, Chaos synchronization of general complex dynamical networks, Physica A, 2004, 334(1–2): 281–302.

    Article  MathSciNet  Google Scholar 

  8. C. Li, W. Sun, and J. Kurths, Synchronization between two coupled complex networks, Phys. Rev. E, 2007, 76(4): 046204.

    Article  Google Scholar 

  9. J. Lü and G. Chen, A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Trans. Autom. Control, 2005, 50(6): 841–846.

    Article  Google Scholar 

  10. C. Li, W. Sun, and D. Xu, Synchronization of complex dynamical networks with nonlinear inner-coupling functions and time delays, Prog. Theor. Phys., 2005, 114(4): 1–13.

    Article  Google Scholar 

  11. F. Sorrentino, M. di Bernardo, F. Garofalo, et al, Controllability of complex networks via pinning, Phys. Rev. E, 2007, 75(4): 046103.

    Article  Google Scholar 

  12. J. Zhou, J. Lu, and J. Lü, Adaptive synchronization of an uncertain complex dynamical network, IEEE Trans. Autom. Control, 2006, 51(4): 652–656.

    Article  Google Scholar 

  13. J. Zhou, T. Chen, and L. Xiang, Adaptive synchronization of coupled chaotic delayed systems based on parameter identification and its applications, Int. J. Bifur. Chaos, 2006, 16(10): 2923–2933.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Zhou, T. Chen, and L. Xiang, Robust synchronization of delayed neural networks based on adaptive control and parameters identification, Chaos Solitons & Fractals, 2006, 27: 905–913.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Zhou and J. Lu, Topology identification of weighted complex dynamical networks, Phys. A, doi: 10.1016/j.physa.2007.07.050.

  16. C. Li, H. Xu, X. Liao, et al., Synchronization in small-world oscillator networks with coupling delays, Physica A, 2004, 335(3–4): 359–364.

    Article  MathSciNet  Google Scholar 

  17. J. Zhou, Z. Liu, and G. Chen, Dynamics of delayed neural networks, Neural N etworks, 2004, 17(1): 87–101.

    Article  MATH  Google Scholar 

  18. C. Li, S. Li, X. Liao, et al., Synchronization in coupled map lattices with small-world delayed interactions, Physica A, 2004, 335(372–4): 365–370.

    Article  MathSciNet  Google Scholar 

  19. W. Wang and J. J. E. Slotine, Contraction analysis of time-delayed communications and group cooperation, IEEE Trans. Autom. Control, 2006, 51(4): 712–717.

    Article  MathSciNet  Google Scholar 

  20. Z. Li, G. Feng, and D. Hill, Controlling complex dynamical networks with coupling delays to a desired orbit, Phys. Lett. A, 2006, 359(1): 42–46.

    Article  MATH  Google Scholar 

  21. W. Lin and H. Ma, Failure of parameter identification based on adaptive synchronization techniques, arXiv: nlin/0701002v2[nlin.AO], 27 Mar. 2007.

  22. H. Lu, Chaotic attractors in delayed neural networks, Phys. Lett. A, 2002, 298(2–3): 109–116.

    Article  MATH  Google Scholar 

  23. M. Jiang, Y. Shen, J. Jian, et al, Stability, bifurcation and a new chaos in the logistic differential equation with delay, Phys. Lett. A, 2006, 350(3–4): 221–227.

    Article  MATH  MathSciNet  Google Scholar 

  24. M. Mackey and L. Glass, Oscillation and chaos in physiological control system, Science, 1977, 197(4300): 287–289.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Wuhan Textile University, Wuhan, 430073, China

    Qunjiao Zhang & Jun’an Lu

Authors
  1. Qunjiao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun’an Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun’an Lu.

Additional information

This work was jointly supported by the National Natural Science Foundation of China under Grant No. 11047114, the Key Project of Chinese Ministry of Education under Grant No. 210141, and the Youth Project of Hubei Education Department under Grant No. Q20101609.

This paper was recommended for publication by Editor Jinhu LÜ.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Q., Lu, J. Exponentially adaptive synchronization of an uncertain delayed dynamical network. J Syst Sci Complex 24, 207–217 (2011). https://doi.org/10.1007/s11424-011-8304-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8304-0

Key words

Search

Navigation