Rabinovich-Fabrikant Equations

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+x

2

)+γx

,

y

t

=x(3z+1-x

2

)+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.