The Moore–Spiegel system is a nonlinear thermo-mechanical oscillator with displacement . The parameter is analogous to the Prandtl number times the Rayleigh number, while is analogous to the Prandtl number times the Taylor number. The system describes a fluid element oscillating vertically in a temperature gradient with a linear restoring force.[more]
The equations of the system are: , , .
Along with the Lorenz system, the Moore–Spiegel system is one of the classical low-order dynamical systems that exhibits chaos.[less]
Snapshots 1, 3, 4, and 5: chaotic time series
Snapshots 2 and 6: periodic time series
 D. W. Moore and E. A. Spiegel, "A Thermally Excited Non-Linear Oscillator," Astrophysical Journal, 143, 1966 pp. 871–887.
 N. J. Balmforth and R. V. Craster, "Synchronizing Moore and Spiegel," Chaos, 7(4), 1997 pp. 738–752.