Simplifications of the Lorenz Attractor
J. C. Sprott
of Wisconsin, Madison
The Lorenz attractor was once thought to be the mathematically simplest
autonomous dissipative chaotic flow, but it is now known that it is
only one member of a very large family of such systems, many of which
are even simpler. Even the system originally proposed by Lorenz is not
in its simplest possible form. This paper will describe a number of
simplifications that can be made to the Lorenz system that preserve its
dynamics as well as a number of chaotic systems that are much simpler
and hence can serve as alternate models of chaos.
Ref: J. C. Sprott, Nonlinear
Psychology, and Life Sciences 13, 271-278 (2009).
The complete paper is available in PDF
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Fig. 1. The Lorenz attractor
Fig. 2. Simplified variants of the Lorenz attractor
Fig. 3. Folded bands
Fig. 4. Jerky Lorenz-like systems