Evidence for low dimensional chaos in sunspot cycles

¹ CORIA/CNRS UMR 6614, Université et INSA de Rouen, Av. de l'Université, BP 12, 76801 Saint-Etienne du Rouvray Cedex, France e-mail: Christophe.Letellier@coria.fr
² Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 31.270-901 Belo Horizonte, MG., Brazil
³ Physics Department, Drexel University, Philadelphia, PA 19104, USA

Received: 29 July 2005
Accepted: 25 November 2005

Abstract

Sunspot cycles are widely used for investigating solar activity. In 1953 Bracewell argued that it is sometimes desirable to introduce the inversion of the magnetic field polarity, and that can be done with a sign change at the beginning of each cycle. It will be shown in this paper that, for topological reasons, this so-called Bracewell index is inappropriate and that the symmetry must be introduced in a more rigorous way by a coordinate transformation. The resulting symmetric dynamics is then favourably compared with a symmetrized phase portrait reconstructed from the z-variable of the Rössler system. Such a link with this latter variable – which is known to be a poor observable of the underlying dynamics – could explain the general difficulty encountered in finding evidence of low-dimensional dynamics in sunspot data.