What is an attractor?
Informally an attractor is simply a state into which a system settles (thus dissipation is needed). Thus in the long term, a dissipative dynamical system may settle into an attractor. Interestingly enough, there is still some controversy in the mathematics community as to an appropriate definition of this term.
Roughly speaking, an attractor is what the behavior of a system settles down to or that to which it is attracted. The attractor forms the limits of the pattern of the system. Imagine that you are taking the pulse, blood pressure and temperature of a person every hour, and you want to graph the relationships among all three vital signs as they change over time. You would construct a graph that was marked at the center by the intersection of three axes, one for each of the vital signs. Connecting these points in temporal sequence forms a trajectory. In nonlinear science, this trajectory is referred to as an attractor.
A preferred position for the system, such that if the system is started from another state it will evolve until it arrives at the attractor, and will then stay there in the absence of other factors. An attractor can be a point (e.g. the centre of a bowl containing a ball), a regular path (e.g. a planetary orbit), a complex series of states (e.g. the metabolism of a cell) or an infinite sequence (called a strange attractor). All specify a restricted volume of state space. The area of state space that leads to an attractor is called its basin of attraction.
