Hidden attractor

Hidden attractors may exist in dynamical systems that are in a state of chaos. Dynamical systems can exist in four states: they can be stable, oscillatory, chaotic, or unstable. These states are achieved by changing elements within the dynamical system itself such as reducing or increasing feedback, friction, or driving or damping forces. A system that is oscillating may repeat itself forever, but a system in chaos does not ever repeat itself. A dynamical system that is oscillating is orderly and predictable; the same dynamical system, driven into a state of chaos, becomes disorderly and unpredictable. However, even when in chaos, dynamical systems, at some hidden level, may have order that ultimately may be important to understanding its future state. Such order may come from a hidden attractor - or several of them. In the plane that we can see, the motion is chaotic, but in another plane the motion is organized and in these planes the points generated by the system may orbit around hidden attractors - so that points that get close to them remain close. For a chaotic system, a hidden attractor can exist as a point, a curve, or a manifold. If a hidden attractor is fractal, it is known as a strange attractor.