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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Volume 28, issue 4
Ann. Geophys., 28, 993–1002, 2010
https://doi.org/10.5194/angeo-28-993-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.
Ann. Geophys., 28, 993–1002, 2010
https://doi.org/10.5194/angeo-28-993-2010
© Author(s) 2010. This work is distributed under
the Creative Commons Attribution 3.0 License.

  21 Apr 2010

21 Apr 2010

Modelling solar cycle length based on Poincaré maps for Lorenz-type equations

H. Lundstedt1 and T. Persson2 H. Lundstedt and T. Persson
  • 1Swedish Institute of Space Physics, Lund, Sweden
  • 2Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

Abstract. Two systems of Lorenz-type equations modelling solar magnetic activity are studied: Firstly a low order dynamic system in which the toroidal and poloidal fields are represented by x- and y-coordinates respectively, and the hydrodynamical information is given by the z coordinate. Secondly a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements.

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