Bifurcation schemes of the Lorenz model (Q1076388)

The Lorenz equations have been investigated by many authors since Lorenz first suggested them as a model for fluid turbulence [J. Atmos. Sci. 20, 130 (1963)]. \textit{C. Sparrow} has published an exhaustive analysis of the dynamics of these equations [The Lorenz equations: bifurcations, chaos, and strange attractors (1982; Zbl 0504.58001)]. In this paper the authors make a global study of these equations which ties together many of the previously studied parameter regimes. In particular, the authors show that the transition to turbulent dynamics need not always occur as in some of the special cases that have been previously described. They present numerical evidence for the existence of tangent bifurcations at the endpoints of period-doubling sequences which do not give rise to intermittent turbulence.