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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