In dynamical systems, an attractor is a value or set of values for the variables of a system to which they will tend towards over enough time, or enough iterations. Examples include fixed-point attractors, periodic attractors (also called limit cycles), and chaotic (also called "strange") attractors.
Limit points are points in the phase space or state space of a system. There are three kinds of limit points: attractors, repellers, and saddle points. A system will tend toward an attractor, and away from a repeller, similar to the way in which a ball rolling across a smooth landscape will roll toward a basin and away from a hill. A saddle point is so-named because it resembles an equestrian saddle. It therefore functions as an attractor to systems originating in "higher" regions, and as a repeller to systems originating from "lower" regions.
- Chaos, Dynamical Systems, Nonlinear Dynamics, Physics, Statistical Physics