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

Author

Listed:
  • R. Idris
  • Z. Siri
  • I. Hashim

Abstract

A chaotic system arising from double‐diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five‐dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

Suggested Citation

  • R. Idris & Z. Siri & I. Hashim, 2013. "On a Five‐Dimensional Chaotic System Arising from Double‐Diffusive Convection in a Fluid Layer," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:428327
    DOI: 10.1155/2013/428327
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    References listed on IDEAS

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    1. Chen, Zhi-Min & Price, W.G., 2006. "On the relation between Rayleigh–Bénard convection and Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 571-578.
    2. Awrejcewicz, J. & Krysko, A.V. & Papkova, I.V. & Krysko, V.A., 2012. "Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents, hyper, hyper-hyper and spatial–temporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 721-736.
    3. Krysko, A.V. & Awrejcewicz, J. & Papkova, I.V. & Krysko, V.A., 2012. "Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 709-720.
    4. Awrejcewicz, J. & Krysko, V.A. & Papkova, I.V. & Krysko, A.V., 2012. "Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 687-708.
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