A fixed point is unstable if nearby points move away from the fixed point under graphical iteration.
|
| Click the picture for an animation. |
A fixed point is unstable if at the fixed point the tangent line to the graph lies outside +45 degrees and -45 degrees.
That is, its slope is greater than +1 or less than -1.
The region between these lines is shaded in blue. If the graph crosses the diagonal outside the blue region (on both sides), the fixed point is stable.
 |
Return to Fixed Points.