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Effects of a magnetic field on chaos for low Prandtl number convection in porous media. (English) Zbl 1215.76087

Summary: The effects of a magnetic field on the route to chaos in a fluid-saturated porous layer were investigated based on the approach of dynamical systems. A low dimensional Lorenz-like model was obtained using Galerkin truncated approximation. The presence of a magnetic field helped delay the convective motion. 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.

MSC:

76S05 Flows in porous media; filtration; seepage
76W05 Magnetohydrodynamics and electrohydrodynamics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E06 Convection in hydrodynamic stability
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