Attractor
In dynamical systems, an
attractor is a set of physical properties toward which a system tends to evolve, regardless of the starting conditions of the system. Property values that get close enough to the attractor values remain close even if slightly disturbed. 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,. 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.