TORI AND CHAOS IN A NONLINEAR DYNAMO MODEL FOR SOLAR ACTIVITY

1 February 1993

journal article
Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos

Vol. 3 (1) , 131-138
https://doi.org/10.1142/s021812749300009x

Abstract

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 T² and T³) and chaotic behavior where a route to chaos via the transition T²⇒T³⇒T²⇒ 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.

Keywords

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