Abstract
Modulation of cyclic magnetic activity associated with grand minima, as well as modulation associated with breaking of dipole or quadrupole symmetry, can be represented in low-order normal form equations. The behaviour found is robust and can be related to similar spatio-temporal patterns in mean field dynamo models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beer, J., Tobias, S.M. and Weiss, N.O. (1998) An active Sun throughout the Maunder Minimum, Solar Phys., 181, pp. 237–249.
Guckenheimer, J. and Holmes, P. (1986) Nonlinear oscillations, dynamical systems and bifurcations of vector fields, 2nd printing, Springer, New York.
Knobloch, E. (1994) Bifurcations in rotating systems, in Lectures on Solar and Planetary Dynamos, M.R.E. Proctor and A.D. Gilbert (eds), Cambridge University Press, Cambridge, pp. 331–372.
Knobloch, E. and Landsberg, A.S. (1996) A new model of the solar cycle, Mon. Not. R. Astron. Soc., 278, pp. 294–302.
Knobloch, E., Tobias, S.M. and Weiss, N.O. (1998) Modulation and symmetry changes in stellar dynamos, Mon. Not. R. Astron. Soc, 297, pp. 1123–1138.
Landsberg, A.S and Knobloch, E. (1996) Oscillatory bifurcation with broken translation symmetry. Phys. Rev. E 53, pp. 3579–3600.
Moehlis, J. and Knobloch, E. (2000) Bursts in oscillatory systems with broken D4 symmetry, Physica D, 135, pp. 263–304.
Parker, E.N. (1993) A solar dynamo surface-wave at the interface between convection and non-uniform rotation, Astrophys. J., 408, pp. 707–719.
Ribes, J.C. and Nesme-Ribes, E. (1993) The solar sunspot cycle in the Maunder minimum AD 1645 to AD 1715. Astron. Astrophys., 276, pp. 549–563.
Tobias, S.M. (1996) Grand Minima in nonlinear dynamos, Astron. Astrophys., 307, pp. L21–L24.
Tobias, S.M. (1997) The solar cycle: parity interactions and amplitude modulation, Astron. Astrophys., 322, pp. 1007–1017.
Tobias, S.M., Weiss, N.O. and Kirk, V. (1995) Chaotically modulated stellar dynamos, Mon. Not. R. Astron. Soc, 273, pp. 1150–1166.
Weiss, N.O. (1993) Bifurcations and symmetry-breaking in simple models of nonlinear dynamos, in The Cosmic Dynamo, F. Krause, K.-H. Rädler and G. Rüdiger (eds), Kluwer, Dordrecht, pp. 219–229.
Weiss, N.O. (1994) Solar and stellar dynamos, in Lectures on Solar and Planetary Dynamos, M.R.E. Proctor and A.D. Gilbert (eds), Cambridge University Press, Cambridge, pp. 59–95.
Weiss, N.O. and Tobias, S.M. (2000) Physical causes of solar activity, Space Sci. Rev., in press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Weiss, N., Knobloch, E., Tobias, S. (2001). Modulation and Symmetry-Breaking in Low-Order Models of the Solar Dynamo. In: Chossat, P., Ambruster, D., Oprea, I. (eds) Dynamo and Dynamics, a Mathematical Challenge. NATO Science Series, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0788-7_45
Download citation
DOI: https://doi.org/10.1007/978-94-010-0788-7_45
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7070-3
Online ISBN: 978-94-010-0788-7
eBook Packages: Springer Book Archive