The Malkus–Robbins dynamo with a linear series motor

Hide [1997] has introduced a number of different nonlinear models to describe the behavior of n-coupled self-exciting Faraday disk homopolar dynamos. The hierarchy of dynamos based upon the Hide et al. [1996] study has already received much attention in the literature (see [Moroz, 2001] for a review). In this paper we focus upon the remaining dynamo, namely Case 3 of [Hide, 1997] for the particular limit in which the Malkus–Robbins dynamo [Malkus, 1972; Robbins, 1997] obtains, but now modified by the presence of a linear series motor. We compare and contrast the linear and the nonlinear behaviors of the two types of dynamo

Unstable periodic orbits of perturbed Lorenz equations

The extended Malkus-Robbins dynamo [Moroz, 2003] reduces to the Lorenz equations when one of the key parameters, $\beta$, vanishes. In a recent study [Moroz, 2004] investigated what happened to the lowest order unstable periodic orbits of the Lorenz limit as $\beta$ was increased to the end of the chaotic regime, using the classic Lorenz parameter values of r = 28; $\sigma$ = 10 and b = 8=3. In this paper we return to the parameter choices of [Moroz, 2003], reporting on two of the cases discussed therein

Unstable periodic orbits of perturbed Lorenz equations

The extended Malkus-Robbins dynamo [Moroz, 2003] reduces to the Lorenz equations when one of the key parameters, $\beta$, vanishes. In a recent study [Moroz, 2004] investigated what happened to the lowest order unstable periodic orbits of the Lorenz limit as $\beta$ was increased to the end of the chaotic regime, using the classic Lorenz parameter values of r = 28; $\sigma$ = 10 and b = 8=3. In this paper we return to the parameter choices of [Moroz, 2003], reporting on two of the cases discussed therein

The extended Malkus-Robbins dynamo as a perturbed Lorenz system

Recent investigations of some self-exciting Faraday-disk homopolar dynamo ([1-4]) 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 [3] and illustrate what happens to some of the lowest order unstable periodic orbits as this parameter is increased from zero