Period stabilization in the Busse–Heikes model of the Küppers–Lortz instability

The Busse–Heikes dynamical model is described in terms of relaxational and non-relaxational 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 Küppers–Lortz instability in determining an alternating period is discussed.