Nonlinear Dynamics

, Volume 68, Issue 1–2, pp 195–205 | Cite as

Topology identification of the modified complex dynamical network with non-delayed and delayed coupling

Original Paper


In practical situations, there exists much uncertain information in complex networks, such as the topological structures and the time delays. So the identification of the topology is an important issue in the research of the complex networks with time delays. In this paper, we consider the problem of identification of the topology of modified complex networks with non-delayed and delayed coupling, and achieve the synchronization of the response networks with the drive networks. Finally, some simulation results are given to show the effectiveness of the method proposed in this paper.


Complex network Topology identification Delayed coupling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Strogatz, S.: Exploring complex networks. Nature 410, 268–276 (2001) CrossRefGoogle Scholar
  2. 2.
    Li, X., Chen, G.: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50, 1381–1390 (2003) CrossRefGoogle Scholar
  3. 3.
    Zhou, J., Chen, T., Xiang, L.: Adaptive synchronization of coupled chaotic systems based on parameters identification and its applications. Int. J. Bifurc. Chaos 16, 2923–2933 (2006) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Zhou, J., Xiang, L., Liu, Z.: Global synchronization in general complex delayed dynamical networks and its applications. Physica A 385, 729–742 (2007) MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhou, J., Xiang, L., Liu, Z.: Synchronization in complex delayed dynamical networks with impulsive effects. Physica A 384, 684–692 (2007) MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wu, X.: Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Physica A 387, 997–1008 (2008) CrossRefGoogle Scholar
  7. 7.
    Zhang, Q., Lu, J., Lü, J., Tse, C.: Adaptive feedback synchronization of a general complex dynamical network with delayed nodes. IEEE Trans. Circuits Syst. II, Express Briefs 55, 183–187 (2008) CrossRefGoogle Scholar
  8. 8.
    Tang, Y., Fang, J., Xia, M., Gu, X.: Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays. Appl. Math. Model. 34, 843–855 (2010) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Tang, Y., Qiu, R., Fang, J., Miao, Q., Xia, M.: Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372, 4425–4433 (2008) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Liang, J., Wang, Z., Liu, X.: Exponential synchronization of stochastic delayed discrete-time complex networks. Nonlinear Dyn. 53, 153–165 (2008) MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Yu, W.: A LMI-based approach to global asymptotic stability of neural networks with time varying delays. Nonlinear Dyn. 48, 165–174 (2007) MATHCrossRefGoogle Scholar
  12. 12.
    Peng, H., Wei, N., Li, L., Xie, W., Yang, Y.: Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control. Phys. Lett. A 374, 2335–2339 (2010) CrossRefGoogle Scholar
  13. 13.
    Lü, L., Meng, L.: Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network. Nonlinear Dyn. (2011). doi: 10.1007/s11071-010-9927-8
  14. 14.
    Lu, J., Cao, J.: Adaptive synchronization of uncertain dynamical networks with delayed coupling. Nonlinear Dyn. 53, 107–115 (2008) MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Zhou, J., Lu, J.: Topology identification of weighted complex dynamical networks. Physica A 386, 481–491 (2007) MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yu, W., Cao, J.: Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks. Chaos 16, 023119 (2006) MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wu, Z., Li, K., Fu, X.: Parameter identification of dynamical networks with community structure and multiple coupling delays. Commun. Nonlinear Sci. Numer. Simul. 15, 3587–3592 (2010) MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Xu, Y., Zhou, W., Fang, J., Lu, H.: Structure identification and adaptive synchronization of uncertain general complex dynamical networks. Phys. Lett. A 374, 272–278 (2009) CrossRefGoogle Scholar
  19. 19.
    Zhou, J., Lu, J., Lü, J.: Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Autom. Control 51, 652–656 (2006) CrossRefGoogle Scholar
  20. 20.
    Liu, H., Lu, J., Lü, J.: Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45, 1799–1807 (2009) MATHCrossRefGoogle Scholar
  21. 21.
    Guo, W., Chen, S., Sun, W.: Topology identification of the complex networks with non-delayed and delayed coupling. Phys. Lett. A 373, 3724–3729 (2009) MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Boyd, S., Ghaoui, L., Feron, E., Balakrishnana, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994) MATHCrossRefGoogle Scholar
  23. 23.
    Peng, H., Li, L., Yang, Y., Sun, F.: Conditions of parameter identification from time series. Phys. Rev. E 83, 036202 (2011) CrossRefGoogle Scholar
  24. 24.
    Sun, F., Peng, H., Xiao, J., Yang, Y.: Identifying topology of synchronous networks by analyzing their transient processes. Nonlinear Dyn. (2011). doi: 10.1007/s11071-011-0081-8
  25. 25.
    Lorenz, E.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963) CrossRefGoogle Scholar
  26. 26.
    Chen, G., Ueta, T.: Yet another chaotic attractor. Int. J. Bifurc. Chaos 9, 1465–1466 (1999) MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Lü, J., Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12, 659–661 (2002) MATHCrossRefGoogle Scholar
  28. 28.
    Liu, C., Liu, T., Liu, L., Liu, K.: A new chaotic attractor. Chaos Solitons Fractals 22, 1031–1038 (2004) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Lu, W., Chen, T., Chen, G.: Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay. Physica D 221, 118–134 (2006) MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Computer School of Wuhan UniversityWuhanP.R. China
  2. 2.Department of Mathematics and FinanceYunyang Teachers’ CollegeShiyanP.R. China
  3. 3.College of Information Science and TechnologyDonghua UniversityShanghaiP.R. China

Personalised recommendations