WOLFRAM|DEMONSTRATIONS PROJECT

Rabinovich-Fabrikant Equations

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plot style
plot
xyz
xy
xz
yz
XYZ background
black
time
t
90.
parameters
γ
0.01
α
0.03
S
0.2
1
5
10
initial positions
x
0
-0.5
y
0
0.
z
0
0.5
The Rabinovich–Fabrikant equations form a set of coupled, nonlinear, first-order differential equations given by:
x
t
=y(z-1+
2
x
)+γx
,
y
t
=x(3z+1-
2
x
)+γy
,
z
t
=-2z(α+xy)
.
This Demonstration lets you explore the solutions to this system. The system parameters,
γ
and
α
, are modified in this Demonstration by adding a parameter scaling factor
S
. By varying these system parameters as well as
the parameter scaling factor and the initial positions
(
x
0,
y
0,
z
0
)
, interesting dynamical events, including chaotic motion, periodic motion, limit cycles, and attractors can be observed in the generated trajectories. These trajectories can be viewed either in three-dimensional space or as projections in two-dimensional planes by changing the plot style. The plot in three dimensions is colored using a gradient in the
z
direction.