Title :
Numerical estimates of local and global motions of the Lorenz attractor
Author :
Kukharenko, Boris G.
Author_Institution :
Mech. Eng. Res. Inst., Acad. of Sci., Moscow, Russia
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.
Keywords :
frequency estimation; time series; Lorenz equations; Lorenz strange attractor; motion estimation; numerical estimation; periodic stable local orbits; real-time attractor; subharmonic transient process; time variant frequency; universal transient processes; Chaos; Conductors; Equations; Frequency; Mechanical engineering; Motion estimation; Nonlinear dynamical systems; Orbits; Spectral analysis; Spine;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1236907