Rabinovich-Fabrikant equations

From Wikipedia, the free encyclopedia

The Rabinovich-Fabrikant equations are a set of three coupled ordinary differential equations exhibiting chaotic behavior for certain values of the parameters. The equations are:

$\dot{x}=y(z-1+x^2)+\gamma x$

$\dot{y}=x(3z+1-x^2)+\gamma y$

$\dot{z}=-2z(\alpha+xy).$

An example of chaotic behavior is obtained for $γ = 0.87$ and $α = 1.1$ . The correlation dimension was found to be 2.19 ± 0.01. (See Grassberger et al. 1983).

[edit] See also

List of chaotic maps

[edit] External links

Weisstein, Eric W. "Rabinovich-Fabrikant Equation." From MathWorld--A Wolfram Web Resource.

[edit] References

P. Grassberger and I. Procaccia (1983). "Measuring the strangeness of strange attractors". Physica D 9: 189-208. (LINK)
Rabinovich, M. I. and Fabrikant, A. L. (1979). "Stochastic Self-Modulation of Waves in Nonequilibrium Media". Sov. Phys. JETP 50: 311.