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Pinning synchronization of complex network with non-derivative and derivative coupling

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Abstract

This paper investigates synchronization of a complex network with non-derivative and derivative coupling. For achieving the pinning synchronization, the corresponding controllers are designed and applied to only a small fraction of nodes. Both linear and adaptive feedback control methods are used to design controllers. Based on Lyapunov stability theory, several simple and useful criteria for pinning synchronization are derived. Finally, numerical simulations are given to verify the effectiveness of the derived results.

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References

  1. Barrat, A., Weight, M.: On the properties of small world networks. Eur. Phys. J. B 13, 547–560 (2000)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Wang, J., Wu, H.: Local and global exponential output synchronization of complex delayed dynamical networks. Nonlinear Dyn. 67, 497–504 (2012)

    Article  MATH  Google Scholar 

  6. Zhou, J., Chen, T.: Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits Syst. I, Regul. Pap. 53, 733–744 (2006)

    Article  MathSciNet  Google Scholar 

  7. Wang, W., Slotine, J.J.E.: Contraction analysis of time-delayed communications and group cooperation. IEEE Trans. Autom. Control 51, 712–717 (2006)

    Article  MathSciNet  Google Scholar 

  8. Wu, J., Jiao, L.: Synchronization in complex dynamical networks with nonsymmetric coupling. Physica D 237, 2487–2498 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sun, W., Yang, Y., Li, C., Fang, J.: Synchronization in delayed map lattices with scale-free interactions. Int. J. Non-Linear Mech. 45, 652–658 (2010)

    Article  Google Scholar 

  10. Zhang, Q., Zhao, J.: Projective and lag synchronization between general complex networks via impulsive control. Nonlinear Dyn. 67, 2519–2525 (2012)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. 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 

  14. Zhou, J., Wu, X., Yu, W., Small, M., Lu, J.: Pinning synchronization of delayed neural networks. Chaos 18, 043111 (2008)

    Article  MathSciNet  Google Scholar 

  15. Zhao, J., Lu, J., Zhang, Q.: Pinning a complex delayed dynamical network to a homogenous trajectory. IEEE Trans. Circuits Syst. II, Express Briefs 56, 514–518 (2009)

    Article  Google Scholar 

  16. Xia, W., Cao, J.: Pinning synchronization of delayed dynamical networks via periodically intermittent control. Chaos 19, 013120 (2009)

    Article  MathSciNet  Google Scholar 

  17. Yu, W., Chen, G., Lü, J.: On pinning synchronization of complex dynamical networks. Automatica 45, 429–435 (2009)

    Article  MATH  Google Scholar 

  18. Xiang, L., Zhu, J.J.H.: On pinning synchronization of general coupled networks. Nonlinear Dyn. 64, 339–348 (2011)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  20. Hu, C., Yu, J., Jiang, H., Teng, Z.: Pinning synchronization of weighted complex networks with variable delays and adaptive coupling weights. Nonlinear Dyn. 67, 1373–1385 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Wen, S., Chen, S., Guo, W.: Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling. Phys. Lett. A 372, 6340–6346 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Xu, Y., Zhou, W., Fang, J., Sun, W.: Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling. Phys. Lett. A 374, 1673–1677 (2010)

    Article  MATH  Google Scholar 

  23. 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 

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Acknowledgements

This work is supported jointly by the Startup Fund for Ph.D. of Jiangxi Normal University (3087) and the Innovation Foundation for Graduate of Jiangxi Province.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, China

    Liping Deng, Zhaoyan Wu & Qingchu Wu

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  1. Liping Deng
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  2. Zhaoyan Wu
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  3. Qingchu Wu
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Correspondence to Zhaoyan Wu.

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Deng, L., Wu, Z. & Wu, Q. Pinning synchronization of complex network with non-derivative and derivative coupling. Nonlinear Dyn 73, 775–782 (2013). https://doi.org/10.1007/s11071-013-0830-y

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  • DOI: https://doi.org/10.1007/s11071-013-0830-y

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