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?