Moore-Spiegel Attractor

max t

80

T

45

R

100

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+R

2

x

)y-Tx

.

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