Quadratic Map Stops Before Denominators Grow - Nonlinear Dynamics and Stability Step by Step

A nonlinear update stays exact by keeping the ledger short. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A nonlinear update can still be exact

With seed one quarter, the training map gives three eighths.

x_{1}=2\cdot\frac{1}{4}\left(1-\frac{1}{4}\right)=\frac{3}{8}

The example stops before fractions become unreadable

The next state is fifteen thirty-seconds; this lesson does not claim a long-run orbit.

x_{2}=2\cdot\frac{3}{8}\left(1-\frac{3}{8}\right)=\frac{15}{32}