A particular solution of a dynamical system to which other solutions converge in time. Attractors can be constant in time, periodic, or have more complex time dependencies (e.g., chaos). They are (asymptotically) stable in the sense that the dynamical system evolves such as to approach the attractor in whose vicinity the system starts out. If the state of a dynamical system is exposed to perturbations, then this attractive property reduces deviations from stable states. It is a stable region in a state space to which the behavior of a system is attracted and where it will eventually settle down. It serves to organise the temporal flow of events through a dynamical system, which can be captured by the topologies of a number of geometrical forms that are two-dimensional (fixed-point and limit-cycle attractors) or three-dimensional (quasi-periodic or torus and chaotic or strange attractors). Attractors can have as many dimensions as the number of variables that influence its system.
See Behavioral state, Bifurcation, Chaos theory, Dynamical system approaches, Mechanism, Non-linear dynamics, Ontogenetic development, Stability, State (or phase) space, Synergetics