Deterministic Chaos
Control of Chaos: Stabilizing a Fixed Point
Suppose we are at the point indicated
on the left picture.
The basic idea of control is to change an available
system parameter (for the tent map, this would be the s-value) so the
modified tent map sends the point to the fixed point of the original tent map.
How do we determine the amount of the modification?
|
| Click either picture to see the tent map adjustment. |
The picture on the right shows how to do this graphically.
Draw a horizontal line from the target point (the nonzero fixed point), and a
vertical line from the starting point.
If the tent map graph passed through the
intersection of these lines, graphical iteration would take us from the
staritng point to the target point.
