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The Extended Malkus–Robbins Dynamo as a Perturbed Lorenz System

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Recent investigations of some self-exciting Faraday-disk homopolar dynamos [Hide, R. and Moroz, I. M., Physica D 134, 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 Chaos 13, 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 Chaos 13, 2003, 147–161] and illustrate what happens to some of the lowest order unstable periodic orbits as this parameter is increased from zero.

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  1. Mathematical Institute, 24–29 St Giles’, Oxford, OX1 3LB, UK

    IRENE M. MOROZ

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  1. IRENE M. MOROZ
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Correspondence to IRENE M. MOROZ.

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MOROZ, I.M. The Extended Malkus–Robbins Dynamo as a Perturbed Lorenz System. Nonlinear Dyn 41, 191–210 (2005). https://doi.org/10.1007/s11071-005-2808-x

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  • DOI: https://doi.org/10.1007/s11071-005-2808-x

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