Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 596251, 8 pages
http://dx.doi.org/10.1155/2013/596251
Research Article

Generalized Synchronization of Different Chaotic Systems Based on Nonnegative Off-Diagonal Structure

1College of Electrical Engineering, Northwest University for Nationalities, Lanzhou 730030, China
2College of Information Science and Engineering, Central South University, Changsha 410075, China
3College of Physics Electrical Information Engineering, Ningxia University, Yinchuan 750021, China

Received 31 May 2013; Accepted 12 September 2013

Academic Editor: Jian Guo Zhou

Copyright © 2013 Ling Guo et al. 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. E. Ott, C. Grebogi, and J. A. Yorke, “Controlling chaos,” Physical Review Letters, vol. 64, no. 11, pp. 1196–1199, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. B. Liu, Y. Zhou, M. Jiang, and Z. Zhang, “Synchronizing chaotic systems using control based on tridiagonal structure,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2274–2281, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. Z. S. Duan, G. R. Chen, and L. Huang, “Synchronization of weighted networks and complex synchronized regions,” Physics Letters A, vol. 372, no. 21, pp. 3741–3751, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Physical Review Letters, vol. 76, no. 11, pp. 1804–1807, 1996. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Taherion and Y. C. Lai, “Observability of lag synchronization of coupled chaotic oscillators,” Physical Review E, vol. 59, no. 6, pp. R6247–R6250, 1999. View at Google Scholar · View at Scopus
  7. J. B. Liu, C. F. Ye, S. J. Zhang, and W. T. Song, “Anti-phase synchronization in coupled map lattices,” Physics Letters A, vol. 274, no. 1-2, pp. 27–29, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. Y. Zhang and J. Sun, “Chaotic synchronization and anti-synchronization based on suitable separation,” Physics Letters A, vol. 330, no. 6, pp. 442–447, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. R. Mainieri and J. Rehacek, “Projective synchronization in three-dimensional chaotic systems,” Physical Review Letters, vol. 82, no. 15, pp. 3042–3045, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. N. Cai, Y. W. Jing, and S. Y. Zhang, “Generalized projective synchronization of different chaotic systems based on antisymmetric structure,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 1190–1196, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. W. Wu, W. J. Zhou, and T. P. Chen, “Cluster synchronization of linearly coupled complex networks under pinning control,” IEEE Transactions on Circuits and Systems I, vol. 56, no. 4, pp. 829–839, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. W. G. Xia and M. Cao, “Clustering in diffusively coupled networks,” Automatica, vol. 47, no. 11, pp. 2395–2405, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. L. Guo, X. H. Nian, Y. Zhao, and Z. S. Duan, “Cluster synchronisation of Lur'e dynamical networks,” IET Control Theory & Applications, vol. 6, no. 16, pp. 2499–2508, 2012. View at Google Scholar
  14. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel, “Generalized synchronization of chaos in directionally coupled chaotic systems,” Physical Review E, vol. 51, no. 2, pp. 980–994, 1995. View at Publisher · View at Google Scholar · View at Scopus
  15. L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Physical Review Letters, vol. 76, no. 11, pp. 1816–1819, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. S. S. Yang and C. K. Duan, “Generalized synchronization in chaotic systems,” Chaos, Solitons and Fractals, vol. 9, no. 10, pp. 1703–1707, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. G. Zhang, Z. R. Liu, and Z. J. Ma, “Generalized synchronization of different dimensional chaotic dynamical systems,” Chaos, Solitons and Fractals, vol. 32, no. 2, pp. 773–779, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. Q. X. Bian and H. X. Yao, “Generalized synchronization between two complex dynamical networks with time-varying delay and nonlinear coupling,” Mathematical Problems in Engineering, vol. 2011, Article ID 978612, 15 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. J. G. Barajas Ramírez, K. P. Cuéllar Galarza, and R. Femat, “Generalized synchronization of strictly different systems: partial-state synchrony,” Chaos, Solitons and Fractals, vol. 45, no. 3, pp. 193–204, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. G. Grassi, “Generalized synchronization between different chaotic maps via dead-beat control,” Chinese Physics B, vol. 21, no. 5, pp. 1–7, 2012. View at Google Scholar
  21. M. P. Aghababa and A. Heydari, “Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities,” Applied Mathematical Modelling, vol. 36, no. 4, pp. 1639–1652, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. S. Acharyya and R. E. Amritkar, “Generalized synchronization of coupled chaotic systems,” The European Physical Journal, vol. 222, no. 3-4, pp. 939–952, 2013. View at Google Scholar
  23. Z. H. Qu, Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles, Springer, London, UK, 2009.
  24. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979.