Moore-Spiegel Attractor

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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.


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.


Contributed by: Milena Cuellar (May 2011)
After work by: E. A. Spiegel (1966)
Open content licensed under CC BY-NC-SA



Snapshots 1, 3, 4, and 5: chaotic time series

Snapshots 2 and 6: periodic time series


[1] D. W. Moore and E. A. Spiegel, "A Thermally Excited Non-Linear Oscillator," Astrophysical Journal, 143, 1966 pp. 871–887.

[2] N. J. Balmforth and R. V. Craster, "Synchronizing Moore and Spiegel," Chaos, 7(4), 1997 pp. 738–752.

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