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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 428327, 10 pages
http://dx.doi.org/10.1155/2013/428327
Research Article

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

1Department of Mathematics, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia
2Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
3School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 19 November 2012; Accepted 14 January 2013

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 R. Idris 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 nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963.
  2. J. Awrejcewicz, Bifurcation and Chaos in Coupled Oscillators, World Scientific, Singapore, 1991. View at Zentralblatt MATH · View at MathSciNet
  3. J. Awrejcewicz and V. A. Krysko, Chaos in Structural Mechanics, Springer, Berlin, Germany, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Qi, S. Du, G. Chen, Z. Chen, and Z. Yuan, “On a four-dimensional chaotic system,” Chaos, Solitons and Fractals, vol. 23, no. 5, pp. 1671–1682, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 7, pp. 1465–1466, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. B. Liu and G. A. Chen, “A new chaotic system and its generation,” International Journal of Bifurcation and Chaos, vol. 13, pp. 261–267, 2003.
  7. J. H. Lü, G. Chen, D. Cheng, and S. Celikovsky, “Bridge the gap between the Lorenz system and the Chen system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 12, pp. 2917–2926, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. M. Chen and W. G. Price, “On the relation between Rayleigh-Bénard convection and Lorenz system,” Chaos, Solitons and Fractals, vol. 28, no. 2, pp. 571–578, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Ookouchi and T. Hada, “Chaotic convection in a simple system modified by differential heating,” Journal of the Physical Society of Japan, vol. 66, pp. 369–378, 1997.
  10. P. Vadasz, “Local and global transitions to chaos and hysteresis in a porous layer heated from below,” Transport in Porous Media, vol. 37, no. 2, pp. 213–245, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  11. P. Vadasz, “Subcritical transitions to chaos and hysteresis in a fluid layer heated from below,” International Journal of Heat and Mass Transfer, vol. 43, pp. 705–724, 2000.
  12. R. Idris and I. Hashim, “Effects of a magnetic field on chaos for low Prandtl number convection in porous media,” Nonlinear Dynamics, vol. 62, no. 4, pp. 905–917, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. N. Mahmud and I. Hashim, “Effects of a magnetic field on chaotic convection in fluid layer heated from below,” International Communications in Heat and Mass Transfer, vol. 38, no. 4, pp. 481–486, 2011.
  14. J. M. Jawdat, I. Hashim, and S. Momani, “Dynamical system analysis of thermal convection in a horizontal layer of nanofluids heated from below,” Mathematical Problems in Engineering, vol. 2012, Article ID 128943, 13 pages, 2012. View at Publisher · View at Google Scholar
  15. H. E. Huppert and J. S. Turner, “Double-diffusive convection,” Journal of Fluid Mechanics, vol. 106, pp. 299–329, 1981.
  16. E. Knobloch, D. R. Moore, J. Toomre, and N. O. Weiss, “Transitions to chaos in two-dimensional double-diffusive convection,” Journal of Fluid Mechanics, vol. 166, pp. 409–448, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. K. Bhattacharjee, Convection and Chaos in Fluids, World Scientific, Singapore, 1987. View at MathSciNet
  18. G. Veronis, “Effect of a stabilizing gradient of solute on thermal convection,” Journal of Fluid Mechanics, vol. 34, pp. 315–336, 1968.
  19. I. N. Sibgatullin, S. Ja. Gertsenstein, and N. R. Sibgatullin, “Some properties of two-dimensional stochastic regimes of double-diffusive convection in plane layer,” Chaos, vol. 13, no. 4, pp. 1231–1241, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. S. Li, Z. W. Chen, and J. M. Zhan, “Double-diffusive Marangoni convection in a rectangular cavity: transition to chaos,” International Journal of Heat and Mass Transfer, vol. 53, pp. 5223–5231, 2010.
  21. J. Awrejcewicz, V. A. Krysko, I. V. Papkova, and A. V. Krysko, “Routes to chaos in continuous mechanical systems. Part 1: mathematical models and solution method,” Chaos, Solitons and Fractals, vol. 45, pp. 687–708, 2012.
  22. V. A. Krysko, J. Awrejcewicz, I. V. Papkova, and A. V. Krysko, “Routes to chaos in continuous mechanical systems. Part 2: modelling transitions from regular to chaotic dynamics,” Chaos, Solitons and Fractals, vol. 45, pp. 709–720, 2012.
  23. J. Awrejcewicz, A. A. Krysko, I. V. Papkova, and A. V. Krysko, “Routes to chaos in continuous mechanical systems. Part 3: the Lyapunov exponents, hyper, hyperhyper and spatial-temporal chaos,” Chaos, Solitons and Fractals, vol. 45, pp. 721–736, 2012.
  24. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D. Nonlinear Phenomena, vol. 16, no. 3, pp. 285–317, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet