The long-term behavior of a system can be represented in the so-called n-dimensional “phase space”. There the specific time development is described through a trajectory, through which the history of the system is recorded. Attraction areas, to which these trajectories aim, are called attractors. Put into other words an attractor is a preferred position for the system to which it evolves no matter what the starting position is. Once such a position is reached it will then stay on the attractor in the absence of other factors.
The existence of an attractor in general means for a scientific process that it possesses the characteristic either to run in a stable, periodical or quasi-periodical way. ‘Stable’ means that the system aims at a certain end condition, called point attractor or the fixed point of the system. On the other hand a process is ‘periodical’ if it repeats itself through a certain interval of time. Finally ‘quasi-periodical’ means that it lasts some time at the beginning until it turns into a periodical behavior - see picture 21.