Skip to main content
SpringerLink
Log in

Synchronization of complex dynamical networks with discontinuous coupling signals

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper concerns with the problem of synchronization of complex dynamical networks (CDNs) with discontinuous coupling signals which are kept constant during the sampling period and are allowed to change only at the sampling instant. Based on the time-dependent Lyapunov functional approach, convex combination technique, and multiple-integral method, a sampling interval- dependent criterion is derived for synchronization of CDNs with discontinuous coupling signals. Numerical examples are given to demonstrate the effectiveness of proposed method and the relation between conservatism of results and triple integral method.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Dorogovtesev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)

    Article  Google Scholar 

  3. Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Erdös, P., Rényi, A.: On random graphs I. Publ. Math. 6, 290–297 (1959)

    MATH  Google Scholar 

  5. Erdös, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61 (1960)

    MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Newman, M.E.J., Watts, D.J.: Renormalization group analysis of the small-world network model. Phys. Lett. A 263, 341–346 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang, L., Wang, Y., Wang, Q., Wang, Q., Zhang, Y.: Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers. Int. J. Control 86, 1766–1776 (2013)

    Article  Google Scholar 

  9. Wu, Z.G., Park, J.H., Su, H., Chu, J.: Non-fragile synchronisation control for complex networks with missing data. Int. J. Control 86, 555–566 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Song, Q., Cao, J., Liu, F.: Synchronization of complex dynamical networks with nonidentical nodes. Phys. Lett. A 374, 544–551 (2010)

    Article  MATH  Google Scholar 

  11. Song, Q., Cao, J.: On pinning synchronization of directed and undirected complex dynamical networks. IEEE Trans. Circuits Syst. I Reg. Pap. 57, 672–680 (2010)

    Article  MathSciNet  Google Scholar 

  12. Li, C., Chen, G.: Synchronization in general complex dynamical networks with coupling delays. Phys. A Stat. Mech. Appl. 343, 263–278 (2004)

    Article  Google Scholar 

  13. Ji, D.H., Lee, D.W., Koo, J.H., Won, S.C., Lee, S.M., Park, J.H.: Synchronization of neutral complex dynamical networks with coupling time-varying delays. Nonlinear Dyn. 65, 349–358 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yang, X., Cao, J., Lu, J.: Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control. IEEE Trans. Circuits Syst. I. Reg. Pap. 59, 371–384 (2012)

    Article  MathSciNet  Google Scholar 

  15. Park, M.J., Kwon, O.M., Park, J.H., Lee, S.M., Cha, E.J.: Synchronization criteria of fuzzy complex dynamical networks with interval time-varying delays. Appl. Math. Comput. 218, 11634–11647 (2012)

  16. Han, X., Lu, J., Wu, X.: Synchronization of impulsively coupled systems. Int. J. Bifurcat. Chaos 18, 1539–1549 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhou, J., Xiang, L., Liu, Z.: Synchronization in complex delayed dynamical networks with impulsive effects. Phys. A 384, 684–692 (2007)

    Article  MathSciNet  Google Scholar 

  18. Yang, M., Wang, Y.W., Xiao, J.W., Wang, H.O.: Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays. Nonlinear Anal. Real World Appl. 11, 3008–3020 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Li, L., Zhang, Y., Hu, J., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74, 805–811 (2011)

    Article  Google Scholar 

  20. Lee, T.H., Wu, Z.G., Park, J.H.: Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control. Appl. Math. Comput. 219, 1354–1366 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wu, Z.G., Shi, P., Su, H., Chu, J.: Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay. IEEE Trans. Neural Netw. Learn. Syst. 24, 1177–1187 (2013)

    Article  Google Scholar 

  22. Wang, Y.W., Xiao, J.W., Wen, C., Guan, Z.H.: Synchronization of continuous dynamical networks with discrete-time communications. IEEE Trans. Neural Netw. 22, 1979–1986 (2011)

    Article  Google Scholar 

  23. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46, 421–427 (2010)

  24. Fridman, E., Blighovsky, A.: Robust sampled-data control of a class of semilinear parabolic systems. Automatica 48, 826–836 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wu, Z.G., Shi, P., Su, H., Chu, J.: Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans. Neural Netw. Learn. Syst. 23, 1368–1376 (2012)

    Article  Google Scholar 

  26. Liu, K., Fridman, E.: Wirtingers inequality and Lyapunov-based sampled-data stabilization. Automatica 48, 102–108 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  27. Seuret, A.: A novel stability analysis of linear systems under asynchronous samplings. Automatica 48, 177–182 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Graham, A.: Kronecker Products and Matrix Calculus: With Applications. Wiley, New York (1982)

    Google Scholar 

  29. Cao, J., Chen, G., Li, P.: Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans. Syst. Man Cybern. B 38, 488–498 (2008)

    Article  Google Scholar 

  30. Fang, M., Park, J.H.: A multiple integral approach to stability of neutral time-delay systems. Appl. Math. Comput. 224, 714–718 (2013)

    Article  MathSciNet  Google Scholar 

  31. Oliveira, M.C.D., Skelton, R.E.: Stability Tests for Constrained Linear Systems. Springer, Berlin (2001)

    Book  Google Scholar 

  32. Park, P.G., Ko, J.W., Jeong, C.: Reciprocally convex approach to stability of systems with time-varying delays. Automatica 47, 235–238 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Park, M.J., Kwon, O.M., Park, J.H., Lee, S.M., Cha, E.J.: Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay. Appl. Math. Comput. 218, 6762–6775 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

Special thanks of Dr. J. H. Park go to W. Lee for all the invested time in lively discussion. This work was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2013R1A1A2A10005201) and in part by Yeungnam University Research Grant.

Author information

Authors and Affiliations

  1. Nonlinear Dynamics Group, Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan, 712-749, Republic of Korea

    Ju H. Park & Tae H. Lee

Authors
  1. Ju H. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tae H. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ju H. Park.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Park, J.H., Lee, T.H. Synchronization of complex dynamical networks with discontinuous coupling signals. Nonlinear Dyn 79, 1353–1362 (2015). https://doi.org/10.1007/s11071-014-1746-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1746-x

Keywords

Search

Navigation