# Rabinovich-Fabrikant Equations

Rabinovich-Fabrikant Equations

The Rabinovich–Fabrikant equations form a set of coupled, nonlinear, first-order differential equations given by:

x

t

2

x

y

t

2

x

z

t

This Demonstration lets you explore the solutions to this system. The system parameters, and , are modified in this Demonstration by adding a parameter scaling factor . By varying these system parameters as well as the parameter scaling factor and the initial positions , 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 direction.

γ

α

S

()

x

0,

y

0,

z

0

z