Sun Dec 16 18:03:49 CET 2007

Chaos and Clipping

It's not so hard to understand the mechanisms of chaos in 3D switched
systems. In fact, they are quite simple to construct:

  * In one (of two) regimes, there is one (2D) mode performing an
    unstable oscillation in a plane together with a (1D) mode that
    decays toward that plane.

  * Put the switching barrier (plane) such that whenever a point
    crosses that plane (due to the unstable 2D oscillation), it is
    attracted fast towards the 2nd regime unstable plane by the
    decaying mode, and will end up close to the unstable fixed point
    of the unstable oscillatory mode.

Maybe linear distorted (clipped) systems are easier to understand as
switched systems too?