The extended Malkus-Robbins dynamo as a perturbed Lorenz system

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. © Springer 2005