Deterministic Chaos

Unstable Fixed Points

A fixed point is unstable if nearby points move away from the fixed point under graphical iteration.
Click the animation to stop.
A fixed point is unstable if at the fixed point the tangent line to the graph lies outside the region between +45° and -45°.
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 unstable.

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