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Mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations

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Abstract

In this paper, it is mainly concerned with the issue of mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. The uncertain terms are the unknown topological structure which exists inside the complex network and the external noise is imposed to the network. In order to achieve the mean square modified function projective synchronization of complex dynamical network, a strict feedback controller and novel adaptive control laws are designed based on Lyapunov stability theory, inequality techniques, and the properties of the Weiner process to obtain several novel synchronization criterion. Furthermore, the effectiveness of the proposed control scheme is validated by numerical simulations.

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References

  1. S.H. Strogatz, Nature 410, 268 (2001)

    Article  ADS  Google Scholar 

  2. X.F. Wang, G.R. Chen, Int. J. Bifurc. Chaos 12, 187 (2002)

    Article  Google Scholar 

  3. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C.S. Zhou, Phys. Rep. 469, 93 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  4. P. Lellis, M. Bernardo, G. Russo, IEEE Trans. Circuits Syst. I 58, 576 (2011)

    Article  Google Scholar 

  5. M.E.J. Newman, A.L. Barabsi, D.J. Watts, The Structure and Dynamics of Complex Networks (Princeton University Press, Princeton, 2006)

  6. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  7. W.W. Yu, P. DeLellis, G.R. Chen, M. di Bernardo, J. Kurths, IEEE Trans. Auto. Contr. 57, 2153 (2012)

    Article  MathSciNet  Google Scholar 

  8. T.P. Chen, X.W. Liu, W.L. Lu, IEEE Trans. Circuits Syst. I 54, 1317 (2007)

    Article  MathSciNet  Google Scholar 

  9. Q.Y. Hu, H.P. Peng, Y.G. Wang, Z.R. Hu, Y.X. Yang, Nonlin. Dyn. 69, 1813 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. J.Q. Hu, J.L. Liang, J.D. Cao, in IEEE fifth International conference on advanced computational intelligence, ICACI, 2012

  11. C.D. Li, X.F. Liao, Phys. Lett. A 329, 301 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  12. G.L. Wen, D.L. Xu, Chaos Sol. Fract. 26, 71 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. R. Zhang, Y.Y. Yang, Z.Y. Xu, M.F. Hu, Phys. Lett. A 374, 3025 (2010)

    Article  ADS  MATH  Google Scholar 

  14. Z.X. Liu, X. Zhang, Z.Q. Chen, Z.Z. Yuan, Int. J. Nonlin. Sci. 7, 95 (2009)

    MATH  MathSciNet  Google Scholar 

  15. Y.R. Liu, Z.D. Wang, J.L. Liang, X.H. Liu, IEEE Trans. Syst. Man Cyber. B 38, 1314 (2008)

    Article  Google Scholar 

  16. H.Y. Du, W. Yao, G. Hu, J. Wang, Adv. Sci. Technol. Lett. 31, 143 (2013)

    Google Scholar 

  17. Y.H. Xu, B. Li, W.N. Zhou, J.A. Fang, Nonlin. Dyn. 70, 289 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. H.Y. Du, Q.S. Zeng, N. Lue, Phys. Lett. A 374, 1493 (2010)

    Article  ADS  MATH  Google Scholar 

  19. T. He, X.L. Lu, X.Q. Wu, J.A. Lu, W.X. Zheng, Physica A 392, 1038 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  20. X.S. Yang, J.D. Cao, Appl. Math. Modell. 34, 3631 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Y.W. Wang, M. Yang, H.O. Wang, Z.H. Guan, IEEE Trans. Circuits Syst. I 56, 2100 (2009)

    Article  MathSciNet  Google Scholar 

  22. X.S. Yang, J.D. Cao, Phys. Lett. A 373, 3259 (2009)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. T.B. Wang, W.N. Zhou, S.W. Zhao, Commun. Nonlin. Sci. Numer. Simulat. 18, 2097 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. X.Z. Jin, G.H. Yang, Commun. Nonlin. Sci. Numer. Simulat. 19, 1985 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  25. H.P. Peng, N. Wei, L.X. Li, W.S. Xie, Y.X. Yang, Phys. Lett. A 374, 2335 (2010)

    Article  ADS  MATH  Google Scholar 

  26. L.X. Li, J. Kurths, H.P. Peng, Y.X. Yang, Q. Luo, Eur. Phys. J. B 86, 125 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  27. W.P. Wang, H.P. Peng, J.H. Xiao, Y.X. Yang, Neural Process. Lett. 41, 71 (2013)

    Article  Google Scholar 

  28. B. Liu, X.L. Wang, H.S. Su, H.T. Zhou, Y.T. Shi, R. Li, Circuits Syst. Signal Process. 33, 1173 (2014)

    Article  MathSciNet  Google Scholar 

  29. X.R. Mao, J. Math. Anal. Appl. 268, 125 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  30. X.R. Mao, Stochastically Differential Equations and Applications (Horwood, Chichester, 1997)

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China

    Hui Zhao & Jinghua Xiao

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, P.R. China

    Lixiang Li, Haipeng Peng & Yixian Yang

Authors
  1. Hui Zhao
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  2. Lixiang Li
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  3. Haipeng Peng
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  4. Jinghua Xiao
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  5. Yixian Yang
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Correspondence to Lixiang Li.

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Zhao, H., Li, L., Peng, H. et al. Mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. Eur. Phys. J. B 88, 15 (2015). https://doi.org/10.1140/epjb/e2014-50577-2

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  • DOI: https://doi.org/10.1140/epjb/e2014-50577-2

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