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Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling

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Abstract

Outer synchronization between the drive network and the response network has attracted much more attention in various fields of science and engineering. In this paper, mixed outer synchronization between two complex dynamical networks with nonidentical nodes and output coupling is investigated via impulsive hybrid control, that is, an adaptive feedback controller with impulsive control effects. Moreover, both the cases of complex networks without and with coupling delay are considered. According to the stability analysis of the impulsive functional differential equation, several sufficient conditions for the networks to achieve mixed outer synchronization are derived. Numerical examples are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.

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References

  1. Huberman, B.A., Adamic, L.A.: Growth dynamics of the world-wide-web. Nature 401, 131–132 (1999)

    Google Scholar 

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

    Article  Google Scholar 

  3. Wang, F., Sun, Y.: Self-organizing peer-to-peer social networks. Comput. Intell. 24, 213–233 (2008)

    Article  Google Scholar 

  4. Chavez, M., Hwang, D.-U., Amann, A., Hentschel, H.G.E., Boccaletti, S.: Synchronization is enhanced in weighted complex networks. Phys. Rev. Lett. 94, 218701 (2005)

    Article  Google Scholar 

  5. Wu, C.W.: Synchronization in Complex Networks of Nonlinear Dynamical Systems. World Scientific, Singapore (2007)

    Book  MATH  Google Scholar 

  6. Stilwell, D., Bollt, E., Roberson, D.: Sufficient conditions for fast switching synchronization in time-varying network topologies. SIAM J. Appl. Dyn. Syst. 5, 140–156 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Sorrentino, F., Ott, E.: Adaptive synchronization of dynamics on evolving complex networks. Phys. Rev. Lett. 100, 114101 (2008)

    Article  Google Scholar 

  8. Ji, D.H., Park, J.H., Yoo, W.J., Won, S.C., Lee, S.M.: Synchronization criterion for Lur’e type complex dynamical networks with time-varying delay. Phys. Lett. A 374, 1218–1227 (2010)

    Article  MATH  Google Scholar 

  9. Gorochowski, T., deBernardo, M., Grierson, C.: Evolving enhanced topologies for the synchronization of dynamical complex networks. Phys. Rev. E 81, 056212 (2010)

    Article  Google Scholar 

  10. Sun, W., Yang, Y., Li, C., Liu, Z.: Synchronization inside complex dynamical networks with double time-delays and nonlinear inner-coupling functions. Int. J. Mod. Phys. B 25, 1531–1541 (2011)

    Article  Google Scholar 

  11. Wang, G., Mu, Z., Wen, C., Li, Y.: A new global stability criteria for neural network with two time-varying delays. Circuits Syst. Signal Process. 31, 177–187 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. deLellis, P., diBernardo, M., Garofalo, F.: Novel decentralized adaptive strategies for the synchronization of complex networks. Automatica 45, 1312–1318 (2009)

    Article  MathSciNet  Google Scholar 

  13. Lu, J., Cao, J.: Adaptive synchronization of uncertain dynamical networks with delayed coupling. Nonlinear Dyn. 53, 107–115 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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  Google Scholar 

  15. Ji, D.H., Jeong, S.C., Park, J.H., Lee, S.M., Won, S.C.: Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling. Appl. Math. Comput. 218, 4872–4880 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang, X., Chen, G.: Pinning control of scale-free dynamical networks. Physica A 310, 521–531 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Li, X., Wang, X., Chen, G.: Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circuits Syst. I, Regul. Pap. 51, 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  18. Chen, T., Liu, X., Lu, W.: Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I, Regul. Pap. 54, 1317–1326 (2007)

    Article  MathSciNet  Google Scholar 

  19. Song, Q., Cao, J., Liu, F.: Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays. Int. J. Robust Nonlinear Control 22, 690–706 (2012)

    Article  MathSciNet  Google Scholar 

  20. Wu, Z., Fu, X.: Cluster mixed synchronization via pinning control and adaptive coupling strength in community networks with nonidentical nodes. Commun. Nonlinear Sci. Numer. Simul. 17, 1628–1636 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Li, P., Cao, J., Wang, Z.: Robust impulsive synchronization of coupled delayed neural networks with uncertainties. Physica A 373, 261–272 (2007)

    Article  Google Scholar 

  23. Dai, Y., Cai, Y., Xu, X.: Synchronisation analysis and impulsive control of complex networks with coupling delays. IET Control Theory Appl. 3, 1167–1174 (2009)

    Article  MathSciNet  Google Scholar 

  24. Han, X.P., Fu, X.L.: Impulsive control induced effects on dynamics of complex networks. Nonlinear Dyn. 3, 203–216 (2010)

    Google Scholar 

  25. Zhou, J., Wu, Q., Xiang, L., Cai, S., Liu, Z.: Impulsive synchronization seeking in general complex delayed dynamical networks. Nonlinear Anal. Hybrid Syst. 5, 513–524 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang, J., Wu, H.: Synchronization criteria for impulsive complex dynamical networks with time-varying delay. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0427-x

    Google Scholar 

  27. Zhou, J., Wu, Q., Xiang, L.: Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0355-9

    MathSciNet  Google Scholar 

  28. Zheng, S.: Analyzing projective synchronization on different scaling factors in a drive-response coupling dynamical network with time-varying delays. Nonlinear Dyn. 70, 709–719 (2012)

    Article  MATH  Google Scholar 

  29. Sorrentino, F., Ott, E.: Network synchronization of groups. Phys. Rev. E 76, 056114 (2007)

    Article  MathSciNet  Google Scholar 

  30. Li, C.P., Sun, W.G., Kurths, J.: Synchronization between two coupled complex networks. Phys. Rev. E 76, 046204 (2007)

    Article  Google Scholar 

  31. Li, C.P., Xu, C.X., Sun, W.G., Xu, J., Kurths, J.: Outer synchronization of coupled discrete-time networks. Chaos 19, 013106 (2009)

    Article  MathSciNet  Google Scholar 

  32. Tang, H., Chen, L., Lu, J., Tse, C.K.: Adaptive synchronization between two complex networks with nonidentical topological structures. Physica A 387, 5623–5630 (2008)

    Article  Google Scholar 

  33. Wu, X., Zheng, W., Zhou, J.: Generalized outer synchronization between complex dynamical networks. Chaos 19, 013109 (2009)

    Article  MathSciNet  Google Scholar 

  34. Sun, W., Chen, Z., Lü, Y., Chen, S.: An intriguing hybrid synchronization phenomenon of two coupled complex networks. Appl. Math. Comput. 216, 2301 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  35. Sun, W., Zhang, J., Li, C.: Synchronization analysis of two coupled complex networks with time delays. Discrete Dynamics in Nature and Society 209321 (2011)

  36. Sun, W., Chen, Z., Lü, J., Chen, S.: Outer synchronization of complex networks with delay via impulse. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0383-5

    Google Scholar 

  37. Wang, J., Ma, Q., Zeng, L., Abd-Elouahab, M.: Mixed outer synchronization of coupled complex networks with time-varying coupling delay. Chaos 21, 013121 (2011)

    Article  MathSciNet  Google Scholar 

  38. Pan, L., Cao, J.: Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal., Real World Appl. 12, 3014 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was jointly supported by the National Science Foundation of China (Grant Nos. 11102076 and 11202085), the Society Science Foundation from Ministry of Education of China (Grant No. 12YJAZH002), and the Foundation of Zhejiang Provincial Education Department (Grant No. Y201328316).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Zhejiang University of Finance & Economics, Hangzhou Zhejiang, 310018, P.R. China

    Song Zheng

  2. School of Economics and International Trade, Zhejiang University of Finance & Economics, Hangzhou Zhejiang, 310018, P.R. China

    Wei Shao

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  1. Song Zheng
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  2. Wei Shao
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Correspondence to Song Zheng.

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Zheng, S., Shao, W. Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling. Nonlinear Dyn 73, 2343–2352 (2013). https://doi.org/10.1007/s11071-013-0945-1

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  • DOI: https://doi.org/10.1007/s11071-013-0945-1

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