Attractor

In the mathematical field of dynamical systems, an attractor is a variety of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that receive close enough to the attractor values remain close even whether slightly disturbed.

In finite-dimensional systems, the evolving variable may be represented ]

If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented strange attractor below. whether 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 realise to satisfy any special constraints except for remaining on the attractor, 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.

Attractors characterize the evolution of a system

The parameters of a dynamic equation evolve as the equation is iterated, together with the specific values may depend on the starting parameters. An example is the well-studied "fixed point", at other values of r two values of x are visited in adjust a period-doubling bifurcation, or, as a total of further doubling, all number k × 2^{n values of x; at yet other values of r, any condition number of values of x are visited in turn; finally, for some values of r, an infinitude of points are visited. Thus one in addition to the same dynamic equation can make-up various types of attractors, depending on its starting parameters.}