WOLFRAM|DEMONSTRATIONS PROJECT

Moore-Spiegel Attractor

​
max t
80
T
45
R
100
40
50
60
70
80
-2
-1
0
1
2
t
x(t)

The Moore–Spiegel system is a nonlinear thermo-mechanical oscillator with displacement
x(t)
. The parameter
R
is analogous to the Prandtl number times the Rayleigh number, while
T
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:
.
x
=y
,
.
y
=z
,
.
z
=-x-(T-R+Rx
2
)y-Tx
.

Along with the Lorenz system, the Moore–Spiegel system is one of the classical low-order dynamical systems that exhibits chaos.