Rabinowitz-Fabrikant Equation

Author

Eric W. Weisstein
April 21, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/Rabinowitz-FabrkiantEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Rabinowitz-FabrkiantEquation.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Numerical Solution

r=Last/@With[{γ=.87,α=1.1},
NDSolve[{
x'[t]==y[t](z[t]-1+((x[t])^2))+γ x[t],
y'[t]==x[t](3z[t]+1-((x[t])^2))+γ y[t],
z'[t]==-2z[t](α+x[t] y[t]),
x[0]==-.03,
y[0]==.2,
z[0]==.1},{x[t],y[t],z[t]},{t,0,10}]
][[1]]

<<Graphics`Colors`

ParametricPlot3D[Append[Function[t,Evaluate[r]][t],Red],{t,0,5}]