Chaos and Order in the Damped Forced Pendulum in a Plane

Apparently simple physical systems often have very complex behavior, as in the case of the damped forced pendulum in a plane, which can have chaotic or nonchaotic behavior. To show this, this Demonstration displays in one graphic various trajectories for distinct initial conditions restricted to a small zone.

In many cases all trajectories have the same form or have a regular form; in other cases the behavior is chaotic, and it is not difficult to see period doubling in the graph.