Tori and Chaos in a Nonlinear Dynamo Model for Solar Activity

A nonlinear dynamo model for solar activity which includes the feedback of the helicity upon the mean magnetic field has been investigated. The qualitative behavior of a seven-dimensional system of ordinary differential equations obtained by truncation of that model has been studied numerically. It has been compared with results from a sixth order system derived from the seventh order system by a special polar coordinate transformation. Depending on characteristic parameters, the seven-dimensional model exhibits periodic, quasiperiodic (on T 2 and T 3 ) and chaotic behavior where a route to chaos via the transition T 2 ⇒T 3 ⇒T 2 ⇒ chaos has been found to be typical. In contrast to that, no chaotic state occurs in the reduced system due to a nonregularity of the coordinate transformation.