Skip to main content

Advertisement

Springer Nature Link
Log in

Synchronization in complex dynamical networks based on the feedback of scalar signals

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper proposes a new approach of synchronization in complex dynamical networks. In this method, the scalar signals are used to instead the output variables of every node as the feedback variables and transmitted signals between every two coupling nodes. As a result, it not only simplifies the topological structure but also saves channel resources at the same time. Especially, some of the criteria are expressed in normal algebraic inequalities instead of matrix inequalities, which means that the original computational effort required is greatly decreased. Finally, several simulation examples are provided to show the effectiveness of the proposed results.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Erdös P, Rényi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17–60

    MATH  Google Scholar 

  2. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-word’ networks. Nature 393:440–442

    Article  Google Scholar 

  3. Almaas E, Kulkarni RV, Stoud D (2002) Characterizing the structure of small-world networks. Phys Rev Lett 89:098101.1–098101.4

    Google Scholar 

  4. Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512

    Google Scholar 

  5. Barabási AL, Albert R (1999) Mean-field theory for scale-free random networks. Physics A 272:173–187

    Article  Google Scholar 

  6. Nian FZ, Wang XY (2010) Efficient immunization strategies on complex networks. J Theor Biol 264:77–83

    Article  MathSciNet  Google Scholar 

  7. Wang MG, Wang XY, Liu ZZ (2010) A new complex network model with hierarchical and modular structures. Chin J Phys 48:805–813

    Google Scholar 

  8. Zhang Y, Wang XY (2012) The fuzzy neural network based on sigmoid chaotic neuron. Chin Phys B 21:020507.1–020507.6

    Google Scholar 

  9. Barahona M, Pecora LM (2002) Synchronization in small-world systems. Phys Rev Lett 89:054101.1–054101.4

    Article  Google Scholar 

  10. Wang XF, Chen GR (2002) Synchronization in small-word dynamical networks. Int J Bifurcation Chaos 12:187–192

    Article  Google Scholar 

  11. Wang XF, Chen GR (2002) Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans Circuits Syst I 49:54–62

    Article  Google Scholar 

  12. Wang XF, Chen GR (2004) Pinning a complex dynamical network to its equilibrium. IEEE Trans Circuits Syst I 51:2074–2087

    Article  Google Scholar 

  13. Wang MJ, Wang XY, Niu YJ (2011) Projective synchronization of a complex network with different fractional order chaos nodes. Chin Phys B 20:010508.1–010508.5

    Google Scholar 

  14. Nian FZ, Wang XY (2010) Chaotic synchronization of hybrid state on complex networks. Int J Mod Phys C 21:457–469

    Article  MathSciNet  MATH  Google Scholar 

  15. Liang Y, Wang XY (2012) Pinning chaotic synchronization in complex networks on maximum eigenvalue of low order matrix. Acta Phys Sin 61:038901.1–038901.8

    Google Scholar 

  16. Chen MY (2006) Some simple synchronization criteria for complex dynamical networks. IEEE Trans Circuits Syst II 53:1185–1189

    Article  Google Scholar 

  17. Fan CX, Jiang GP, Jiang FH (2010) Synchronization between two complex networks using scalar signals under pinning control. IEEE Trans Circuits Syst I 57:2991–2998

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  19. Zhou J, Lu JA, Lü JH (2008) Pinning adaptive synchronization of a general complex dynamical network. Automatica 44:996–1003

    Article  Google Scholar 

  20. Jiang GP, Wallace KT, Chen GR (2006) A state-observer-based approach for synchronization in complex dynamical networks. IEEE Trans Circuits Syst I 53:2739–2745

    Article  Google Scholar 

  21. Wu JS, Jiao LC (2007) Observer-based synchronization in complex dynamical networks with nonsymmetric coupling. Phys A 386:469–480

    Article  MathSciNet  Google Scholar 

  22. Luo Q, Wu W, Li LX, Yang YX, Peng HP (2008) Adaptive synchronization research on the uncertain complex networks with time-delay. Acta Phys Sin 57:1529–1534

    MathSciNet  MATH  Google Scholar 

  23. Chen MY, Zhou DH (2006) Synchronization in uncertain complex networks. Chaos 16:013101.1–013101.8

    Google Scholar 

  24. Wu JS, Jiao LC (2008) Synchronization in dynamica networks with nonsymmetrical time-delay coupling based on linear feedback controllers. Phys A 387:2111–2119

    Article  MathSciNet  Google Scholar 

  25. Li CG, Chen GR (2004) Synchronization in general complex dynamical networks with coupling delays. Phys A 343:263–278

    Article  MathSciNet  Google Scholar 

  26. Wu JS, Jiao LC (2008) Global synchronization and state tuning in asymmetric complex dynamical networks. IEEE Trans Circuits Syst II 55:932–936

    Google Scholar 

  27. Wu JS, Jiao LC (2008) Synchronization in complex dynamical networks with nonsymmetric coupling. Phys D 237:2487–2498

    Article  MathSciNet  MATH  Google Scholar 

  28. Lancaster P, Tismenetsky M (1985) The theory of matrices second edition with application. Academic Press, San Diego

    Google Scholar 

  29. Khalil HK (2002) Nonlinear systems. Prentice Hall, New Jeysey

    MATH  Google Scholar 

  30. Chen GR, Lü JH (2003) Analysis, control, and synchronize on the dynamic systems of Lorenze. Science Press, China (in Chinese)

    Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (60804006, 50977008 and 60821063).

Author information

Authors and Affiliations

  1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Mo Zhao, Huaguang Zhang & Zhiliang Wang

Authors
  1. Mo Zhao
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Huaguang Zhang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Zhiliang Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Mo Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, M., Zhang, H. & Wang, Z. Synchronization in complex dynamical networks based on the feedback of scalar signals. Neural Comput & Applic 23, 683–689 (2013). https://doi.org/10.1007/s00521-012-0964-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-0964-8

Keywords