  Two low-dimensional magnetohydrodynamic models containing three velocity and
three magnetic modes are described. One of them (nonhelical model) has zero
kinetic and current helicity, while the other model (helical) has nonzero
kinetic and current helicity. The velocity modes are forced in both these
models. These low-dimensional models exhibit a dynamo transition at a critical
forcing amplitude that depends on the Prandtl number. In the nonhelical model,
dynamo exists only for magnetic Prandtl number beyond 1, while the helical
model exhibits dynamo for all magnetic Prandtl number. Although the model is
far from reproducing all the possible features of dynamo mechanisms, its
simplicity allows a very detailed study and the observed dynamo transition is
shown to bear similarities with recent numerical and experimental results.
