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 equations with two quadratic nonlinearities.  This paper reviews efforts over the subsequent years to discover even simpler examples of chaotic flows.  There is reason to believe that the algebraically simplest examples of chaotic flows with quadratic and piecewise linear nonlinearities have now 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 (2000)

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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