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Author(s):
N. Bekki and T. Karakisawa
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Title:
Bifurcations from Periodic Solution in a Simplified Model of Two-dimensional
Magnetoconvection
Date of publication:
Jan. 1995
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Key words:
Boussinesq fluid, Rayleigh-Benard convection, Bifurcation, Period-doubling, Heteroclinic, Intermittency, Chaos, Holmes-Melnikov boundary
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Abstract:
We study a two dimensional Boussinesq fluid with the nonlinear interaction between the Rayleigh-Benard convection and an externally imposed magnetic field. We introduce a simplified model of fifth-order system of nonlinear ordinary differential equations with five parameters and integrate it numerically in some parameter regions. We find various types of bifurcations from periodic solutions:period-doubling bifurcation, heteroclinic bifurcation, intermittency and abnormal transition to chaos. We also derive a normal form equation from our fifth-order system, applying the center manifold theory to it, and give an expression for the renormalized Holmes-Melnikov boundary to evaluate numerical results. By means of the normal form equation, we show that each property of the two phase portraits described by the Duffing equation and the van der Pol equation emanates from one common attractor in the five-dimensional space of the fifth-order system.
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