thumb|Trajectory of a solution with parameter values <math>\alpha=0.05</math> and <math>\gamma=0.1</math> and initial conditions <math>x_0=0.1</math>, <math>y_0=-0.1</math>, and <math>z_0=0.1</math>, using the default ODE solver in MATLAB. Colors vary from blue to yellow with time.

thumb|Trajectory of a solution with parameter values <math>\alpha=0.05</math> and <math>\gamma=0.1</math> and initial conditions <math>x_0=0.1</math>, <math>y_0=-0.1</math>, and <math>z_0=0.1</math>, using the default ODE solver in Mathematica. Colors vary from orange-red to magenta-red with time. Notice the drastic change in the solutions with respect to the solution obtained with MATLAB.

thumb|A chaotic attractor found with parameter values <math>\alpha=1.1</math> and <math>\gamma=0.87</math> and initial conditions <math>x_0=-1</math>, <math>y_0=-0</math>, and <math>z_0=0.5</math>, using the default ODE solver in Mathematica. Colors vary from orange-red to magenta-red with time. Notice that colors do not follow any order, reflecting the chaotic dynamics of the solution.

The Rabinovich–Fabrikant equations are a set of three coupled ordinary differential equations exhibiting chaotic behaviour for certain values of the parameters. They are named after Mikhail Rabinovich and Anatoly Fabrikant, who described them in 1979.

System description

The equations are:

Equilibrium points

thumb|Graph of the regions for which equilibrium points <math>\tilde{\mathbf{x_{1,2,3,4}</math> exist.

The Rabinovich–Fabrikant system has five hyperbolic equilibrium points, one at the origin and four dependent on the system parameters α and γ:

</references>

  • Weisstein, Eric W. "Rabinovich–Fabrikant Equation." From MathWorld—A Wolfram Web Resource.
  • Chaotics Models a more appropriate approach to the chaotic graph of the system "Rabinovich–Fabrikant Equation"