Skip to main content
SpringerLink
Log in

Synchronization-based topology identification of uncertain stochastic delay complex networks

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the itô formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

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. Watts D J, Strogatz S H. Collective dynamics of small-world networks [J]. Nature, 1998, 393(6684): 440–442.

    Article  PubMed  CAS  Google Scholar 

  2. Barabási A L, Albet R. Emergence of scaling in random networks [J]. Science, 1999, 286(5439): 509–512.

    Article  PubMed  Google Scholar 

  3. Boccaletti S, Latora V, Moreno Y, et al. Complex networks: structure and dynamics [J]. Physics Reports, 2006, 424(4): 175–308.

    Article  Google Scholar 

  4. Liu Z X, Chen Z Q, Yuan Z Z. Pinning control of weighted general complex dynamical networks with time delay [J]. Physica A: Statistical Mechanics and Its Applications, 2007, 375(1): 345–354.

    Article  Google Scholar 

  5. Yang H, Sheng L. Pinning control of a generalized complex dynamical network model [J]. Journal of Control Theory and Applications, 2009, 7(1): 1–8.

    Article  CAS  Google Scholar 

  6. Zhou T, Kuscsik Z, Liu J, et al. Solving the apparent diversity-accuracy dilemma of recommender systems [J]. PNAS, 2010, 107(10): 4511–4515.

    Article  PubMed  CAS  Google Scholar 

  7. Wu X, Lu H. Cluster synchronization in the adaptive complex dynamical networks via a novel approach [J]. Physics Letters A, 2011, 375(14): 1559–1565.

    Article  CAS  Google Scholar 

  8. Guan Z H, Yang S H, Yao J. Stability analysis and H ∞ control for hybrid complex dynamical networks with coupling delays [J]. International Journal of Robust and Nonlinear Control, 2012, 22(2): 205–222.

    Article  Google Scholar 

  9. Wu Z Y, Li K Z, Fu X C. Parameter identification of dynamical networks with community structure and multiple coupling delays [J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(11): 3587–3592.

    Article  Google Scholar 

  10. Guo S J, Fu X C. Estimating topology of discrete dynamical networks [J]. Communications in Theoretical Physics, 2010, 54(1): 181–185.

    Article  Google Scholar 

  11. Si G, Sun Z, Zhang H, et al. Parameter estimation and topology identification of uncertain fractional order complex networks [J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17(12): 5158–5171.

    Article  Google Scholar 

  12. Zhang S, Wang R S, Zhang X S. Identification of overlapping community structure in complex networks using fuzzy c-means clustering [J]. Physica A: Statistical Mechanics and Its Applications, 2007, 374(1): 483–490.

    Article  Google Scholar 

  13. Zhou J, Lu J. Topology identification of weighted complex dynamical networks [J]. Physica A: Statistical Mechanics and Its Applications, 2007, 386(1): 481–491.

    Article  Google Scholar 

  14. Huang J. Chaos synchronization between two novel different hyperchaotic systems with unknown parameters [J]. Nonlinear Analysis: Theory, Methods & Applications, 2008, 69(11): 4174–4181.

    Article  Google Scholar 

  15. Xu Y, Zhou W, Fang J, et al. Structure Identification and adaptive synchronization of uncertain general complex dynamical networks [J]. Physics Letters A, 2009, 374(2): 272–278.

    Article  CAS  Google Scholar 

  16. Yu D. Estimating the topology of complex dynamical networks by steady state control: Generality and limitation [J]. Automatica, 2010, 46(12): 2035–2040.

    Article  Google Scholar 

  17. Xu Y, Zhou W, Fang J, et al. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions [J]. Commun Nonlinear Sci Number, 2011, 16(8): 3337–3343.

    Article  Google Scholar 

  18. Wang Z, Liu Y, Li M, et al. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays [J]. Neural Networks, IEEE Transactions on, 2006, 17(3): 814–820.

    Article  Google Scholar 

  19. Wu X. Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay [J]. Physica A: Statistical Mechanics and Its Applications, 2008, 387(4): 997–1008.

    Article  Google Scholar 

  20. Liu H, Lu J A, Lü J, et al. Structure identification of uncertain general complex dynamical networks with time delay [J]. Automatica, 2009, 45(8): 1799–1807.

    Article  Google Scholar 

  21. Øksendal B. Stochastic Differential Equations: An Introduction with Applications [M]. New York: Springer-Verlag, 2010.

    Google Scholar 

  22. Lu J, Cao J. Synchronization-based approach for parameters identification in delayed chaotic neural networks [J]. Physica A: Statistical Mechanics and Its Applications, 2007, 382(2): 672–682.

    Article  Google Scholar 

  23. Gong G, Qian M. Application of Random Process-and the Random Model in Algorithm and Intelligent Computer [M]. Beijing: Tsinghua University Press, 2004(Ch).

    Google Scholar 

  24. Yang J, Zhong S, Luo W. Mean square stability analysis of impulsive stochastic differential equations with delays [J]. Journal of Computational and Applied Mathematics, 2008, 216(2): 474–483.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430081, Hubei, China

    Hongfang Liu, Lilan Tu & Le Yu

Authors
  1. Hongfang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lilan Tu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Le Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lilan Tu.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (60904060 and 61104127)

Biography: LIU Hongfang, female, Master candidate, research direction: topology identification of complex network.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, H., Tu, L. & Yu, L. Synchronization-based topology identification of uncertain stochastic delay complex networks. Wuhan Univ. J. Nat. Sci. 18, 337–342 (2013). https://doi.org/10.1007/s11859-013-0939-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-013-0939-3

Key words

CLC number

Search

Navigation