Some Simple Chaotic Jerk Functions

J. C. Sprott
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
(Received 9 September 1996; accepted 3 January 1997)

ABSTRACT

A numerical examination of third-order, one-dimensional, autonomous, differential equations with quadratic and cubic nonlinearities has uncovered a number of algebraically simple equations involving time-dependent accelerations (jerks) that have chaotic solutions. Properties of some of these systems are described, and suggestions are given for further study.

Ref: J. C. Sprott, Am. J. Phys. 65, 537-543 (1997)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.

Fig. 1. Strange attractor for Eq. (9), with A = 2.017.
[Figure 1]

Fig. 2. Strange attractor for Eq. (11), with A = 2.017.
[Figure 2]

Fig. 3. Strange attractor for Eq. (15), with A = 0.5 and B = 0.25.
[Figure 3]

Fig. 4. Poincare section at x'' = 0 for Eq. (16), with B =0.01.
[Figure 4]

Fig. 5. Strange attractor for Eq. (21), with A = 0.25.
[Figure 5]

Fig. 6. Strange attractor for Eq. (22), with A = 3.6.
[Figure 6]

Fig. 7. Poincare section at x'' = 0 for Eq. (23), with A = 0.01.
[Figure 7]

GIF animated views of the attractor in Fig. 1 and its basin of attraction are available.