In the
mathematical field of
dynamical systems, an
attractor is a set of states 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.
Dynamical systems in the physical world tend to arise from
dissipative systems: if it were not for some driving force, the motion would cease. (Dissipation may come from
internal friction,
thermodynamic losses, or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the
phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee.
Invariant sets and
limit sets are similar to the attractor concept. An
invariant set is a set that evolves to itself under the dynamics. Attractors may contain invariant sets. A
limit set is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.