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Mathematical Problems in Engineering
Volume 2016, Article ID 2850651, 13 pages
http://dx.doi.org/10.1155/2016/2850651
Research Article

Low Model Analysis and Synchronous Simulation of the Wave Mechanics

College of Science, Liaoning University of Technology, Jinzhou 121001, China

Received 11 May 2016; Accepted 13 July 2016

Academic Editor: Bernard Bonello

Copyright © 2016 Wenyuan Duan 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. N. Lorenz, “Deterministic non-periods flows,” Atoms Science, vol. 20, pp. 130–141, 1963. View at Google Scholar
  2. Y. Shu, Y. Zhang, and H. Xu, “Control and synchronization of general Lorenz chaotic system,” Journal of Chongqing Institute of Technology (Natural Sciences), vol. 22, no. 8, pp. 54–61, 2008. View at Google Scholar
  3. D. G. Thomas, B. Khomami, and R. Sureshkumar, “Nonlinear dynamics of viscoelastic Taylor-Couette flow: effect of elasticity on pattern selection, molecular conformation and drag,” Journal of Fluid Mechanics, vol. 620, pp. 353–382, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. W.-S. Kim, “Application of Taylor vortex to crystallization,” Journal of Chemical Engineering of Japan, vol. 47, no. 2, pp. 115–123, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. H. L. Swinney and J. P. Gollub, Hydrodynamic Instabilities and the Transition to Turbulence, Springer, Berlin, Germany, 1981.
  6. G. I. Taylor, “Stability of a viscons liquid contained between two rotating cylinders,” Philosophical Transactions of the Royal Society of London A, vol. 223, pp. 289–343, 1923. View at Google Scholar
  7. H. Liu and B. Jiang, “Chaos control of gear system with elostomeric web based on multi-parameter multistep method,” Journal of Harbin Institute of Technology, vol. 19, no. 5, pp. 23–30, 2012. View at Google Scholar
  8. G. R. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, World Scientific, Singapore, 1998. View at MathSciNet
  9. H. L. Swinney and J. P. Gollub, Hydrodynamic, Instablilities and the Transition to Turbulence, Springer, Berlin, Germany, 1981.
  10. H. Y. Wang, “The Chaos behavior and simulation of three-model systems of Couette-Taylor flow,” Acta Mathematica Scientia. Series A, vol. 35, no. 4, pp. 769–779, 2015. View at Google Scholar · View at MathSciNet
  11. S. Liu, “The wave mechanics in chaos and atmospheric turbulence,” Science in China (Series B), vol. 5, 1986. View at Google Scholar
  12. 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 · View at Scopus
  13. L. M. Pecora and T. L. Carroll, “Driving systems with chaotic signals,” Physical Review A, vol. 44, no. 4, pp. 2374–2383, 1991. View at Publisher · View at Google Scholar · View at Scopus
  14. D.-Y. Chen, C. Wu, C.-F. Liu, X.-Y. Ma, Y.-J. You, and R.-F. Zhang, “Synchronization and circuit simulation of a new double-wing chaos,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1481–1504, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Chen, W. Zhao, X. Liu, and X. Ma, “Synchronization and antisynchronization of a class of chaotic systems with nonidentical orders and uncertain parameters,” Journal of Computational and Nonlinear Dynamics, vol. 10, no. 1, Article ID 011003, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Guckenheimer, Nonlinear Oscillation, Dynamical Systems, and Bifurcation of Vector Fields, Springer, Berlin, Germany, 1983.
  17. J. H. Ge and J. Xu, “Hopf bifurcation and chaos in an inertial neuron system with coupled delay,” Science China Technological Sciences, vol. 56, no. 9, pp. 2299–2309, 2013. View at Publisher · View at Google Scholar · View at Scopus
  18. H. A. El-Saka, E. Ahmed, M. I. Shehata, and A. M. A. El-Sayed, “On stability, persistence, and Hopf bifurcation in fractional order dynamical systems,” Nonlinear Dynamics, vol. 56, no. 1-2, pp. 121–126, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. X. Liao, “On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization,” Science in China, Series E: Information Sciences, vol. 34, no. 12, pp. 1404–1419, 2004. View at Google Scholar
  20. L. Huang, Theory and Application of the Stability and Robustness, National Defend Industy Press, Beijing, China, 2000.
  21. A. A. Martynyuk, “Elements of the theory of stability of hybrid systems (review),” International Applied Mechanics, vol. 51, no. 3, pp. 243–302, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. X. Liao, The Stability Theory and Application of Dynamical System, National Defend Industy Press, Beijing, China, 2000.
  23. V. I. Vorotnikov and Yu. G. Martyshenko, “On partial stability theory of nonlinear dynamic systems,” Journal of Computer and Systems Sciences International, vol. 49, no. 5, pp. 702–709, 2010. View at Publisher · View at Google Scholar
  24. J. Fang, “Chaos control method, synchronization principle and its application prospect in nonlinear system (two),” Progress in Physics, vol. 16, no. 2, pp. 137–159, 1996. View at Google Scholar