Qualitative understanding of the Lorenz equations through a well-known second order dynamical system

Abstract

In the present paper we show how it is possible to reduce the Lorenz system, modeling the onset of turbulence in the Bénard problem, to a well-known dynamical system on a two-dimensional manifold. The reduction is made by applying in a skillful way the center manifold theory. In such a way one obtains a syntetic qualitative description of some relevant aspects of the phase portraits and of the bifurcations in the original system.