Attractor - Revision history

Karl Jones at 11:30, 21 April 2016

2016-04-21T11:30:45Z

Karl Jones: /* Description */

2016-02-05T16:42:40Z

‎Description

Karl Jones: First

2015-08-31T12:19:02Z

First

New page

In the [[Mathematics|mathematical]] field of [[dynamical systems]], 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.

== Description ==

TO DO ...

In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.

If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of [[chaos theory]].

A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, backward and forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor).

== See also ==

* [[Chaos theory]]
* [[Strange attractor]]

== External links ==

* [https://en.wikipedia.org/wiki/Attractor Attractor] @ Wikipedia

← Older revision		Revision as of 11:30, 21 April 2016
Line 19:		Line 19:

	* [https://en.wikipedia.org/wiki/Attractor Attractor] @ Wikipedia		* [https://en.wikipedia.org/wiki/Attractor Attractor] @ Wikipedia
		+
		+	[[Category:Chaos theory]]
		+	[[Category:Fractals]]
		+	[[Category:Mathematics]]

← Older revision		Revision as of 16:42, 5 February 2016
Line 4:		Line 4:

	== Description ==		== Description ==
−
−	~~TO DO ...~~

	In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.		In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.