Algebraically Simple Chaotic Flows
J. C. Sprott
Department of Physics, University
of Wisconsin, Madison, Wisconsin 53706, USA
Stefan J. Linz
Theoretische Physik I, Instit fur Physik, Universitat Augsburg,
D-86135 Augsburg, Germany
(Manuscript invited: November 27, 1999; accepted April 2, 2000)
It came as a surprise to most scientists when Lorenz in 1963 discovered
chaos in a simple system of three autonomous ordinary differential
with two quadratic nonlinearities. This paper reviews efforts
the subsequent years to discover even simpler examples of chaotic
There is reason to believe that the algebraically simplest examples of
chaotic flows with quadratic and piecewise linear nonlinearities have
been identified. The properties of these and other simple systems
will be described.
Ref: J. C. Sprott and S. J. Linz, Int. J.
Chaos Theory and Appl. 5, 3-22
A manuscript of the complete paper is available in PDF
and Postscript formats.
This paper has been expanded into a 304-page book
with 280 examples of simple chaotic flows.
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