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On the relation between Rayleigh–Bénard convection and Lorenz system

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  • Chen, Zhi-Min
  • Price, W.G.

Abstract

Based on an extension of the Lorenz truncation scheme, a chaotic mathematical model is developed to provide a profile of the chaotic attractor associated with the Rayleigh–Bénard convection problem in a plane fluid motion. The attractor of the Lorenz system is a cross-section of the attractor of the proposed model, in which solutions always exist in circles mirroring those appearing in the convection problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:571-578
    DOI: 10.1016/j.chaos.2005.08.010
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    Cited by:

    1. Panchev, S. & Spassova, T. & Vitanov, N.K., 2007. "Analytical and numerical investigation of two families of Lorenz-like dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1658-1671.
    2. Vitanov, Nikolay K. & Sakai, Kenshi & Dimitrova, Zlatinka I., 2008. "SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 187-202.
    3. Allan, Fathi M. & Syam, Mohammad I., 2009. "Numerical investigation of the instability of Benard problem," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1552-1558.
    4. Lakshmi, B.S. & Ramana Murty, M.V., 2007. "Airy function approximations to the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1433-1435.

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