Periodic Solutions and Bifurcation Structure at High <i>R</i> in the Lorenz Model

Abstract

A stable periodic solution of the Lorenz system in the limit as $R \to \infty $ is computed as a fixed point of a Poincaré mapping. The solution is shown to exist for finite R by application of the implicit function theorem. Successive bifurcations as R is decreased to the nonperiodic regime are examined numerically.