Abstract
Bifurcations from oscillatory solutions are studied in a truncated model of two-dimensional Boussinesq magnetoconvection. The fifth order system of nonlinear differential equations is integrated numerically and in certain parameter regimes there is a bifurcation from symmetrical to asymmetrical oscillations followed by a period-doubling cascade. After the accumulation point there is a semiperiodic cascade leading to chaotic behaviour. Then the semiperiodic cascade is repeated in reverse, followed by a period-halving cascade and a bifurcation back to symmetry. Finally, the branch of oscillatory solutions terminates with a symmetrical heteroclinic orbit that connects two saddle-foci. The interval with aperiodic solutions contains many pairs of narrow windows with asymmetrical or symmetrical periodic solutions, each with its own cascade. This pattern of behaviour is likely to occur when a periodic orbit approaches a symmetrical pair of saddle-foci with eigenvalues that satisfy Shil'nikov's inequality.
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