The status that a dynamic system eventually "settles down to". An attractor is a set of values in the phase space to which a system migrates over time, or iterations. An attractor can be a single fixed point, a collection of points regularly visited, a loop, a complex orbit, or an infinite number of points. It need not be one- or two-dimensional. Attractors can have as many dimensions as the number of variables that influence its system.
An attractor is a trajectory of a dynamical system such that initial conditions nearby it will tend toward it in forward time. Often called a stable attractor but this is redundant.
An attractor of a map is a set of points which ``attracts'' orbits, from some set of initial points of nonzero probability of being selected. To be precise, an attractor of a map is an indecomposable closed invariant set with the property that, given , there is a set of positive Lebesgue measure in the -neighbourhood of such that if is in then the -limit set of orb() is contained in and the orbit of is contained in [ 10].
(physics) a point in the ideal multidimensional phase space that is used to describe a system toward which the system tends to evolve regardless of the starting conditions of the system
a model representation of the behavioral results of a system
a particular space to which a system converges, it can be compared with a dissipative structure
a point or area in phase space that seems to suck in the solutions of a non-linear system when the equation you are using for the non-linear system is iterated
a 'set', 'curve', or 'space' that a system irreversibly evolves to if left undisturbed
a set of measure zero but its basin of attraction has a non-zero measure
a set of points in the state space that the dynamic system converges toward as time approaches infinity
a single point, usually outside the bounding box, that the plant has a tendency to grow towards
a solution to a set of equations towards which a dynamical system tends
a state towards which a system is drawn
A point to which a system tends to move, a goal, either deliberate or constrained by system parameters (laws). The three standard attractor types are fixed point, cyclic and strange (or chaotic).
a set of numerical values toward which the result of an iterated function is drawn, or attracted
Dissipative dynamical systems are characterized by the presence of some sort of internal "friction" that tends to contract phase-space volume elements. Contraction in phase space allows such systems to approach a subset of the phase-space called an attractor as the elapsed time grows large. Attractors therefore describe the long-term behavior of a dynamical system. Steady state (or equilibrium) behavior corresponds to fixed-point attractors, in which all trajectories starting from the appropriate basin-of-attraction eventually converge onto a single point. For linear dissipative dynamical systems, fixed point attractors are the only possible type of attractor. Nonlinear systems, on the other hand, harbor a much richer spectrum of attractor types. For example, in addition to fixed-points, there may exist periodic attractors such as limit cycles. There is also an intriguing class of chaotic attractors called strange attractors that have a complicated geometric structure (see Chaos and Fractals).
A term used in modern dynamics to denote a limit towards which trajectories of change within a dynamical system move. Attractors generally lie within basins of attraction. Attractors and basins of attraction are essential features of the mathematical models of morphogenetic fields due to Rene Thom.
Dynamical equilibrium of a DS * Attracts all nearby points * Three types: static (point), periodic (cyclic), chaotic
A region in an outcome basin to which the dynamics of a system tends to take it. The size and shape of the attractor depends, sensitively, upon key parameters and the dynamics to which it is driven by such parameters. An attractor may occupy space between dimensions; if so, it is said to be a fractal.
Usually a graphically depicted relationship of states of a non-linear system over time. There are several types of attractor.
A stable equilibrium state having the property that small departures from the equilibrium continually diminish. An attractor may be represented in a coordinate system as a single point (the usual case) or as a bounded set of infinitely many points (as in the case of a limit cycle). A strange attractor is an attractor containing an infinite number of points and having the property that small changes in neighboring states give rise to large and apparently unpredictable changes in the evolution of the system. The best-known example of a strange attractor in meteorology is that discovered by E. N. Lorenz (1963) in solutions to a simplified set of equations describing the motion of air in a horizontal layer heated from below. Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130–141.
A set of states (points in the phase space), invariant under the dynamics, towards which neighboring states in a given basin of attraction asymptotically approach as the motion of the dynamic system evolves. An attractor is defined as the smallest unit which cannot be itself decomposed into two or more attractors with distinct basins of attraction. This restriction is necessary since a dynamical system may have multiple attractors, each with its own basin of attraction.
A characterization of the long-term behavior of a dissipative dynamical system.
In information systems, a Web site that, over time, continues to attract a large number of visitors.
In dynamical systems, an attractor is a set to which the system evolves after a long enough time. For the set to be an attractor, trajectories that get close enough to the attractor must remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with fractal structures known as a strange attractor.
