The truncated mean field dynamo equations exhibit chaotic behaviour, and can provide a reasonable model of the solar cycle (Schmalz and Stix, 1991). Truncations can produce oscillatory, quasiperiodic, chaotic, and constant solutions. However these models have the problem that the introduction of additional fourier terms as the level of truncation is increased can result in different types of behaviour. It is possible that the most interesting behaviour (such as chaos) may disappear as the level of truncation is increased. (Schmalz and Stix, 1991, Covas et al 1997)
Using normal form theory it should be possible to derive a model with behaviour that is more robust. The results of such low order models would be generic within the normal form framework, and so likely to be observed in a wide range of dynamo models.
A model exhibiting the bifurcation structure shown below as a stars evolution is tracked backwards in time (i.e. as the dynamo number is increased) would result a dynamo that mimics observed behaviour in stars.
Here we look at the set of equations first used to model dynamos in Tobias S.M., Weiss N.O., Kirk V., 1995, MNRAS 273 1150-1166. This is a (relatively) simple set of normal form equations which has this bifurcation structure. Details about the equations from a more mathematical point of view can be found in Kirk V., 1991, Phys. Lett.A, 154, 243, as well as Kirk V., 1993, Physica, 66D, 267.