Physica D 62 (1993) 323-337.
Chaos in a low-order model of magnetoconvection
A.M.Rucklidge
Department of Applied Mathematics and Theoretical Physics,
University of Cambridge, Cambridge, CB3 9EW, UK
Abstract.
In the limit of tall, thin rolls, weakly nonlinear convection in a vertical
magnetic field is described by an asymptotically exact third-order set of
ordinary differential equations. These equations are shown here to have three
codimension-two bifurcation points: a Takens-Bogdanov bifurcation, at which a
gluing bifurcation is created; a point at which the gluing bifurcation is
replaced by a pair of homoclinic explosions between which there are Lorenz-like
chaotic trajectories; and a new type of bifurcation point at which the first of
a cascade of period-doubling bifurcation lines originates. The last two
bifurcation points are analysed in terms of a one-dimensional map. The
equations also have a T-point, at which there is a heteroclinic connection
between a saddle and a pair of saddle-foci; emerging from this point is a line
of Shil'nikov bifurcations, involving homoclinic connections to a saddle-focus.
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