Abstract
Centre manifold theory, a useful tool in the study of dynamical systems, plays a crucial role in analysing the stability of the system. In the paper the three-dimensional manifold arising in the study of Rayleigh-Bénard-Brinkman convection in enclosures is reduced to a unidimensional manifold using a transformation dictated by the centre manifold theorem. Such a reduction is possible since the Lorenz model is autonomous. The advantage in this procedure is that the intractable Lorenz model gets reduced to a tractable Ginzburg-Landau equation and hence facilitates an analytical study of heat transport.
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Siddheshwar, P.G., Manjunath, S., Sushma, T.S. (2019). Solution of the Lorenz Model with Help from the Corresponding Ginzburg-Landau Model. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_6
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DOI: https://doi.org/10.1007/978-3-030-01123-9_6
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