Science China Technological Sciences

, Volume 62, Issue 1, pp 94–105 | Cite as

Identifying topologies and system parameters of uncertain time-varying delayed complex networks

  • Xiong Wang
  • HaiBo Gu
  • QianYao Wang
  • JinHu LüEmail author


Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors. Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.


system parameters and network topologies identification anticipatory synchronization uncertain time-varying delayed complex networks noise-perturbed complex networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barabási A L. The New Science of Networks. Cambridge, Massachusetts: Perseus Publishing, 2002Google Scholar
  2. 2.
    Strogatz S H. Exploring complex networks. Nature, 2001, 410: 268–276CrossRefzbMATHGoogle Scholar
  3. 3.
    Albert R, Barabási A L. Statistical mechanics of complex networks. Rev Mod Phys, 2002, 74: 47–97MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wang X F, Chen G R. Complex networks: Small-world, scale-free and beyond. IEEE Circuits Syst Mag, 2003, 3: 6–20CrossRefGoogle Scholar
  5. 5.
    Watts D J, Strogatz S H. Collective dynamics of “small-world” networks. Nature, 1998, 393: 440–442CrossRefzbMATHGoogle Scholar
  6. 6.
    Chen Y, Lü J, Lin Z. Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica, 2013, 49: 1768–1775MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chen Y, Lü J, Yu X, et al. Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J Control Optim, 2013, 51: 3274–3301MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chen Y, Lü J. Delay-induced discrete-time consensus. Automatica, 2017, 85: 356–361MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lü J, Chen G. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans Automat Contr, 2005, 50: 841–846MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Liu K, Duan P, Duan Z, et al. Leader-following consensus of multiagent systems with switching networks and event-triggered control. IEEE Trans Circuits Syst I, 2018, 65: 1696–1706CrossRefGoogle Scholar
  11. 11.
    Yu D, Righero M, Kocarev L. Estimating topology of networks. Phys Rev Lett, 2006, 97: 188701CrossRefGoogle Scholar
  12. 12.
    Boccaletti S, Latora V, Moreno Y, et al. Complex networks: Structure and dynamics. Phys Rep, 2006, 424: 175–308MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zhou J, Lu J. Topology identification of weighted complex dynamical networks. Physica A, 2007, 386: 481–491MathSciNetCrossRefGoogle Scholar
  14. 14.
    Wu X, Wang W, Zheng W X. Inferring topologies of complex networks with hidden variables. Phys Rev E, 2012, 86: 046106CrossRefGoogle Scholar
  15. 15.
    Jansen R, Yu H, Greenbaum D, et al. A bayesian networks approach for predicting protein-protein interactions from genomic data. Science, 2003, 302: 449–453CrossRefGoogle Scholar
  16. 16.
    Marwan N, Romano M C, Thiel M, et al. Recurrence plots for the analysis of complex systems. Phys Rep, 2007, 438: 237–329MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wang W X, Yang R, Lai Y C, et al. Predicting catastrophes in nonlinear dynamical systems by compressive sensing. Phys Rev Lett, 2011, 106: 154101CrossRefGoogle Scholar
  18. 18.
    Han X, Shen Z, Wang W X, et al. Robust reconstruction of complex networks from sparse data. Phys Rev Lett, 2015, 114: 028701CrossRefGoogle Scholar
  19. 19.
    Wu X, Zhao X, Lu J, et al. Identifying topologies of complex dynamical networks with stochastic perturbations. IEEE Trans Control Netw Syst, 2016, 3: 379–389MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Wang Y F, Wu X Q, Feng H, et al. Topology inference of uncertain complex dynamical networks and its applications in hidden nodes detection. Sci China Tech Sci, 2016, 59: 1232–1243CrossRefGoogle Scholar
  21. 21.
    Zhang S, Wu X, Lu J A, et al. Recovering structures of complex dynamical networks based on generalized outer synchronization. IEEE Trans Circuits Syst I, 2014, 61: 3216–3224CrossRefGoogle Scholar
  22. 22.
    Wang Y, Wu X, Feng H, et al. Inferring topologies via driving-based generalized synchronization of two-layer networks. J Stat Mech, 2016, 2016: 053208MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wu Y, Liu L. Exponential outer synchronization between two uncertain time-varying complex networks with nonlinear coupling. Entropy, 2015, 17: 3097–3109CrossRefGoogle Scholar
  24. 24.
    Che Y, Li R X, Han C X, et al. Adaptive lag synchronization based topology identification scheme of uncertain general complex dynamical networks. Eur Phys J B, 2012, 85: 265CrossRefGoogle Scholar
  25. 25.
    Al-mahbashi G, Noorani M S M, Bakar S A, et al. Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance. Neurocomputing, 2016, 207: 645–652CrossRefGoogle Scholar
  26. 26.
    Che Y, Li R, Han C, et al. Topology identification of uncertain nonlinearly coupled complex networks with delays based on anticipatory synchronization. Chaos, 2013, 23: 013127MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Yang X L, Wei T. Revealing network topology and dynamical parameters in delay-coupled complex network subjected to random noise. Nonlinear Dyn, 2015, 82: 319–332MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Voss H U. Anticipating chaotic synchronization. Phys Rev E, 2000, 61: 5115–5119CrossRefGoogle Scholar
  29. 29.
    Cao J D, Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuits Syst I, 2005, 52: 417–426MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Wu X. Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay. Physica A, 2008, 387: 997–1008CrossRefGoogle Scholar
  31. 31.
    Liu H, Lu J A, Lü J, et al. Structure identification of uncertain general complex dynamical networks with time delay. Automatica, 2009, 45: 1799–1807MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Sun Y, Li W, Ruan J. Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation. Commun Nonlinear Sci Numer Simul, 2013, 18: 989–998MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Mao X. Stochastic versions of the LaSalle theorem. J Differ Equ, 1999, 153: 175–195MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Lu J, Cao J. Synchronization-based approach for parameters identification in delayed chaotic neural networks. Physica A, 2007, 382: 672–682CrossRefGoogle Scholar
  35. 35.
    Khalil H K. Nonlinear Systems. 3rd ed. NJ: Prentice Hall, 2002zbMATHGoogle Scholar
  36. 36.
    Liu K, Zhu H, Lü J. Cooperative stabilization of a class of LTI plants with distributed observers. IEEE Trans Circuits Syst I, 2017, 64: 1891–1902MathSciNetCrossRefGoogle Scholar
  37. 37.
    Chen S K, Yu S M, Lü J H, et al. Design and FPGA-based realization of a chaotic secure video communication system.. IEEE Trans Circuits Syst Video Technol, 2018, 28: 2359–2371CrossRefGoogle Scholar
  38. 38.
    Lü J, Chen G. A new chaotic attractor coined. Int J Bifur Chaos, 2002, 12: 659–661MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xiong Wang
    • 1
    • 2
  • HaiBo Gu
    • 1
    • 2
  • QianYao Wang
    • 1
    • 2
  • JinHu Lü
    • 1
    • 3
    Email author
  1. 1.LSC, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.School of Automation Science and Electrical Engineering, State Key Laboratory of Software Development Environment, and Beijing Advanced Innovation Center for Big Data and Brain ComputingBeihang UniversityBeijingChina

Personalised recommendations