Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability

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.