# Some Simple Chaotic Flows

J. C. Sprott

*Department of Physics, University
of Wisconsin, Madison, Wisconsin 53706*

(Received 17 January 1994)
### ABSTRACT

A systematic examination of general three-dimensional autonomous
ordinary
differential equations with quadratic nonlinearities has uncovered 19
distinct
simple examples of chaotic flows with either five terms and two
nonlinearities
or six terms and one nonlinearity. The properties of these systems are
described, including their critical points, Lyapunov exponents, and
fractal
dimensions.
Ref: J. C. Sprott, Phys. Rev. E **50**,
R647-R650
(1994)

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TABLE I. Algebraically simple three-dimensional ODE's with chaotic
solutions.

Fig. 1. Poincare section at *z* = 0 for the conservative
chaotic
case A in Table I.

Fig. 2. Stereoscopic plot of the trajectory for the case B chaotic
attractor
in Table I.

Fig. 3. Stereoscopic plot of the trajectory for the case N chaotic
attractor
in Table I.

GIF animations of all 19 of the systems listed above are available.