Details

The original equations describing the system are given by:

,

,

,

,

where and are the self-inductances of the coils, and are the resistances, and are the electric currents, and are the angular velocities, and are the moments of inertia, and and are the driving forces.

Taking for simplicity

, , , , ,

and making the substitutions

, , , , ,

with the parameter , we obtain

,

,

.

The Rikitake system exhibits Lorenz-type chaos while orbiting around two unstable fixed points.

References

[1] T. Rikitake, "Oscillations of a System of Disk Dynamos," Mathematical Proceedings of the Cambridge Philosophical Society, 54(1), 1958 pp. 89–105. doi: 10.1017/S0305004100033223.

[2] J. A. Jacobs, Reversals of Earth's Magnetic Field, New York: Cambridge University Press, 1994.

[3] I. Pehlivan, Y. Uyaroglu, and S. Coskun, "Simulation and Realization of the Rikitake Attractor's Chaotic Oscillator Circuit," Proceedings of the 5th International Advanced Technologies Symposium (IATS’09), May 13–15, 2009, Karabuk, Turkey. iats09.karabuk.edu.tr/press/bildiriler_pdf/IATS09_02-01_ 480.pdf.