Solution of the Lorenz Model with Help from the Corresponding Ginzburg-Landau Model

  • P. G. SiddheshwarEmail author
  • S. Manjunath
  • T. S. Sushma
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Rayleigh-Bénard-Brinkman convection Center manifold Enclosure 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • P. G. Siddheshwar
    • 1
    Email author
  • S. Manjunath
    • 2
  • T. S. Sushma
    • 2
  1. 1.Department of MathematicsBangalore UniversityBangaloreIndia
  2. 2.Department of MathematicsB. N. M. Institute of TechnologyBangaloreIndia

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