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 starting point to the target point.