  The Busse-Heikes dynamical model is described in terms of relaxational and
nonrelaxational dynamics. Within this dynamical picture a diverging alternating
period is calculated in a reduced dynamics given by a time-dependent
Hamiltonian with decreasing energy. A mean period is calculated which results
from noise stabilization of a mean energy. The consideration of
spatial-dependent amplitudes leads to vertex formation. The competition of
front motion around the vertices and the Kuppers-Lortz instability in
determining an alternating period is discussed.
