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Journal of Applied Mathematics
Volume 2012, Article ID 595360, 12 pages
http://dx.doi.org/10.1155/2012/595360
Research Article

Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators

1College of Science, Guilin University of Technology, Guilin 541004, China
2Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin 541004, China

Received 14 March 2012; Accepted 15 June 2012

Academic Editor: Jitao Sun

Copyright © 2012 Zhen Jia and Guangming Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature, vol. 391, no. 4, pp. 440–442, 1998. View at Google Scholar
  2. A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” American Association for the Advancement of Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar
  3. S. H. Strogatz, “Exploring complex networks,” Nature, vol. 410, pp. 268–276, 2001. View at Google Scholar
  4. J. M. Pujol, J. Bejar, and J. Delgado, “Clustering algorithm for determining community structure in large networks,” Physical Review E, vol. 74, Article ID 016107, 9 pages, 2006. View at Google Scholar
  5. S. Wasserman and K. Faust, Social Network Analysis, Cambridge University Press, Cambridge, UK, 1994.
  6. K. Kaneko, “Relevance of dynamic clustering to biological networks,” Physica D, vol. 75, pp. 55–73, 1994. View at Google Scholar
  7. M. E. J. Newman, “Clustering and preferential attachment in growing networks,” Physical Review E, vol. 64, Article ID 016131, 13 pages, 2001. View at Publisher · View at Google Scholar
  8. Y. Zhang and J. Sun, “Robust synchronization of coupled delayed neural networks under general impulsive control,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1476–1480, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. V. N. Belykh, I. V. Belykh, and M. Hasler, “Connection graph stability method for synchronized coupled chaotic systems,” Physica D, vol. 195, no. 1-2, pp. 159–187, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Yu. Pogromsky, “A partial synchronization theorem,” Chaos, vol. 18, no. 3, Article ID 037107, 2008. View at Publisher · View at Google Scholar
  11. Y. C. Kouomou and P. Woafo, “Cluster synchronization in coupled chaotic semiconductor lasers and application to switching in chaos-secured communication networks,” Optics Communications, vol. 223, pp. 273–282, 2003. View at Google Scholar
  12. W. Yu, J. Cao, G. Chen, J. Lu, J. Han, and W. Wei, “Local synchronization of a complex network model,” IEEE Transactions on Systems, Man, and Cybernetics C, vol. 39, no. 1, pp. 230–241, 2009. View at Google Scholar
  13. Y. C. Kouomou and P. Woafo, “Transitions from spatiotemporal chaos to cluster and complete synchronization ststes in a shift-invariant set of coupled nonlinear oscillators,” Physical Review E, vol. 67, no. 4, part 2, Article ID 046205, 2003. View at Google Scholar
  14. W. Qin and G. Chen, “Coupling schemes for cluster synchronization in coupled Josephson equations,” Physica D, vol. 197, no. 3-4, pp. 375–391, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. V. Belykh, I. Belykh, and E. Mosekilde, “Cluster synchronization models in an ensemble of coupled chaotic oscil-lators,” Physical Review E, vol. 63, Article ID 036216, 2001. View at Google Scholar
  16. V. N. Belykh, G. V. Osipov, V. S. Petrov, J. A. K. Suykens, and J. Vandewalle, “Cluster synchronization in oscillatory networks,” Chaos, vol. 18, no. 3, p. 037106, 2008. View at Publisher · View at Google Scholar
  17. X. Lu, B. Qin, and X. Lu, “New approach to cluster synchronization in complex dynamical networks,” Communications in Theoretical Physics, vol. 51, pp. 485–489, 2009. View at Google Scholar
  18. L. Chen and J. Lu, “Cluster synchronization in a complex dynamical network with two nonidentical clusters,” Journal of Systems Science & Complexity, vol. 21, no. 1, pp. 20–33, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. M. Krstic, I. Kanellakopouls, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, NY, USA, 1995.
  20. Z. Li, L. C. Jiao, and J. J. Lee, “Robust adaptive global synchronization of complex dynamical networks by adjusting time-varying coupling strength,” Physica A, vol. 387, no. 5-6, pp. 1369–1380, 2008. View at Publisher · View at Google Scholar
  21. E. N. Lorenz, “Determinstic non-periods flows,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  22. A. Chen, J. Lu, J. Lü et al., “Generating hyperchaotic Lü attractor via state feedback control,” Physica A, vol. 364, pp. 103–110, 2006. View at Publisher · View at Google Scholar
  23. J. Sun, “Some global synchronization criteria for coupled delay-systems via unidirectional linear error feedback approach,” Chaos, Solitons and Fractals, vol. 19, no. 4, pp. 789–794, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. X. Wan and J. Sun, “Adaptive-impulsive synchronization of chaotic systems,” Mathematics and Computers in Simulation, vol. 81, no. 8, pp. 1609–1617, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH