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Bifurcations and Symmetry-Breaking in Simple Models of Nonlinear Dynamos

Published online by Cambridge University Press:  19 July 2016

N.O. Weiss
N.O. Weiss*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Cambridge CB3 9EW, U.K.

Abstract

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Low-order models of nonlinear dynamos can be used to investigate generic properties of more realistic mean field dynamos. Reducing the partial differential equations to a set of ordinary differential equations makes it possible to explore the bifurcation structure in considerable detail and to compute unstable solutions as well as ones that are stable. Complicated time-dependent behaviour is typically associated with a homoclinic or heteroclinic bifurcation. Destruction of periodic orbits at saddles or saddle-foci gives rise to Lorenz-like or Shil'nikov-like chaotic oscillations, while destruction of a quasiperiodic orbit leads to aperiodically modulated cycles. Changes in spatial symmetry can also be investigated. The interaction between solutions (steady or periodic) with dipole and quadrupole symmetry gives rise to a complicated bifurcation structure, with several recognizably different mixed-mode solutions; similar behaviour has also been found in spherical dynamo models. These results have implications for the expected behaviour of stellar dynamos.

Type
6. General Aspects of Dynamo Theory
Information
Symposium - International Astronomical Union , Volume 157: The Cosmic Dynamo , 1993 , pp. 219 - 229
Copyright
Copyright © Kluwer 1993 

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