Rabinovich-Fabrikant equations

Rabinovich-Fabrikant equations

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 gamma=0.87 and alpha=1.1. The correlation dimension was found to be 2.19 ± 0.01.(See Grassberger et al. 1983).

ee also

* List of chaotic maps

External links

* Weisstein, Eric W. [http://mathworld.wolfram.com/Rabinovich-FabrikantEquation.html "Rabinovich-Fabrikant Equation."] From MathWorld--A Wolfram Web Resource.

References

* [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1983PhyD....9..189G&db_key=PHY (LINK)]
*


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Mikhail Rabinovich — Mikhail Izrailevich Rabinovich (MIR) (Russian: Михаил Израилевич Рабинович (MИР); born April 20, 1941) is an influential physicist and neuroscientist working in the field of nonlinear dynamics and its applications. His work helped shape the… …   Wikipedia

  • Chaos theory — This article is about chaos theory in Mathematics. For other uses of Chaos theory, see Chaos Theory (disambiguation). For other uses of Chaos, see Chaos (disambiguation). A plot of the Lorenz attractor for values r = 28, σ = 10, b = 8/3 …   Wikipedia

  • List of mathematics articles (R) — NOTOC R R. A. Fisher Lectureship Rabdology Rabin automaton Rabin signature algorithm Rabinovich Fabrikant equations Rabinowitsch trick Racah polynomials Racah W coefficient Racetrack (game) Racks and quandles Radar chart Rademacher complexity… …   Wikipedia

  • List of chaotic maps — In mathematics, a chaotic map is a map that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete time or a continuous time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”