The Lorenz system and its generalizations as dynamo models with memory

The one of the known applications of the classical Lorenz system is an axisymmetric αω-dynamo with a dynamical quenching of the α-effect by the helicity. In this paper we consider generalizations of the Lorentz system, which are the models of α2 - and α2ω-dynamo. The cases of finite and infinite memory in the quenching functional are considered. The conditions for the existence of stationary dynamo regimes and regimes of regular and chaotic inversions are analytically and numerically studded