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.