Nonlinear Dynamics

, Volume 41, Issue 1–3, pp 191–210 | Cite as

The Extended Malkus–Robbins Dynamo as a Perturbed Lorenz System

Article

Recent investigations of some self-exciting Faraday-disk homopolar dynamos [Hide, R. and Moroz, I. M., Physica D134, 1999, 387–301; Moroz, I. M. and Hide, R., International Journal of Bifurcation and Chaos 2000, 2701–2716; Moroz, I. M., International Journal of Bifurcation and Chaos13, 2003, 147–161; Moroz, I. M., International Journal of Bifurcation and Chaos, to appear] have yielded the classic Lorenz equations as a special limit when one of the principal bifurcation parameters is zero. In this paper we focus upon one of those models [Moroz, I. M., International Journal of Bifurcation and Chaos13, 2003, 147–161] and illustrate what happens to some of the lowest order unstable periodic orbits as this parameter is increased from zero.

Key Words

dynamos Lorenz equations unstable periodic orbits 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematical InstituteOxfordUK

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