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.
[Table]

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

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

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

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