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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