Heteroclinic Networks in Rotating Convection
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.