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.