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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 529251, 9 pages
doi:10.1155/2012/529251
Research Article

Adaptive Control and Synchronization of the Shallow Water Model

P. Sangapate

Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand

Received 6 July 2011; Revised 24 September 2011; Accepted 26 September 2011

Academic Editor: Carlo Cattani

Copyright © 2012 P. Sangapate. 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. J. Tribbia, An Introduction to Three-Dimensional Climate Modeling, Oxford University, New York, NY, USA, 1992.
  2. 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 MathSciNet
  3. J. H. Park and O. M. Kwon, “A novel criterion for delayed feedback control of time-delay chaotic systems,” Chaos, Solitons and Fractals, vol. 23, no. 2, pp. 495–501, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. L. Liao and S. H. Tsai, “Adaptive synchronization of chaotic systems and its application to secure communications,” Chaos, Solitons and Fractals, vol. 11, no. 9, pp. 1387–1396, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. T. Yang and L. O. Chua, “Generalized synchronization of chaos via linear transformations,” International Journal of Bifurcation and Chaos, vol. 9, no. 1, pp. 215–219, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. G. Yu and S. Zhang, “Adaptive backstepping synchronization of uncertain chaotic system,” Chaos, Solitons and Fractals, vol. 27, no. 3, pp. 643–649, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. 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 MathSciNet
  8. M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators, World Scientific Publishing, River Edge, NJ, USA, 1996.
  9. S. K. Han, C. Kerrer, and K. Kuramoto, “Dephasing and brusting in coupled neutral oscillators,” Physical Review Letters, vol. 75, pp. 3190–3193, 1995. View at Publisher · View at Google Scholar
  10. B. Blasius, A. Huppert, and L. Stone, “Complex dynamics and phase synchronization in spatially extended ecological systems,” Nature, vol. 399, no. 6734, pp. 354–359, 1999. View at Publisher · View at Google Scholar · View at PubMed
  11. K. Murali and M. Lakshmanan, “Secure communication using a compound signal from generalized synchronizable chaotic systems,” Physical Review Letters, vol. 241, no. 6, pp. 303–310, 1998. View at Zentralblatt MATH
  12. M. Feki, “An adaptive chaos synchronization scheme applied to secure communication,” Chaos, Solitons and Fractals, vol. 18, no. 1, pp. 141–148, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York, NY, USA, 1989.