Numerical estimates of local and global motions of the Lorenz attractor

Abstract

The Lorenz equations are studied numerically. It is shown that the Lorenz strange attractor can comprise attraction domains, or real-time attractors in the vicinity of a stable fixed point, and transient sets or conductors, which are related to jumps between the fixed points. It has been found that long sequences of nearly periodic stable local orbits near each stable fixed point of the Lorenz equations are real-time attractors for the Lorenz attractor. The laws of motion are revealed for these sequences of local orbits. The backbone curves are found for three universal transient processes, which represent all long sequences of local orbits of the Lorenz attractor. It has been found that the conductors of the Lorenz attractor are represented by nearly subharmonic transient process for 3 time-variables defined by the Lorenz equations.