Difference between revisions of "Strange attractor"
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Revision as of 08:11, 13 September 2015
In the mathematical field of dynamical systems, a strange attractor is an attractor which as has a fractal structure.
This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist.
Contents
Attractors
An attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
Strange attractor behavior
If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together.
Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.
Origin
The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow.
Differentiability
Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.
Noise
Strange attractors may also be found in presence of noise, where they may be shown to support invariant random probability measures of Sinai-Ruelle-Bowen type.
Examples
Examples of strange attractors include:
- Double-scroll attractor
- Hénon attractor
- Rössler attractor
- Tamari attractor
- Lorenz attractor - named after Edward Norton Lorenz
See also
External links
- Strange attractor @ Wikipedia
