Three Branches of Dynamo Action
  In addition to the weak-dipolar state and to the fluctuating-multipolar state, widely discussed in the literature, a third regime has been identified in Dormy (2016). It corresponds to a strong-dipolar branch which appears to approach, in a numerically affordable regime, the magnetostrophic limit relevant to the dynamics of the Earth's core. We discuss the transitions between these states and point to the relevance of this strong-dipolar state to Geodynamo modelling. 
Emmanuel Dormy, Ludivine Oruba, Ludovic Petitdemange
physics.geo-ph