__Heteroclinic
Networks in Rotating Convection__

__Claire Postlethwaite__

DAMTP, University of Cambridge,UK

Motivated by the problem of pattern formation in rotating thermal convection,
we consider two coupled Busse-Heikes cycles that occur when the dynamics are
restricted to roll amplitudes with wave vectors confined to a planar hexagonal
superlattice. Different types of coupling can lead to heteroclinic networks
comprising many heteroclinic cycles. Each equilibrium in the network now has an
unstable manifold with dimension greater than one, and hence none of the cycles
can be asymptotically stable. However, the network as a whole can still be
asymptotically stable, and individual cycles can have strong attractive
properties. We investigate conditions for a given cycle to be 'preferred' and
examine bifurcations that can occur. We find that for some parameter values, switching
between cycles occurs, and this can lead to trajectories cycling between the
cycles.