 Ricker population map

The Ricker population map models density-dependent reproduction with a declining per-capita growth factor. Its nonzero equilibrium is $K$, with multiplier $1-r$. It loses stability through a period-doubling bifurcation at $r=2$. Every population after the first update is bounded by $K{e}^{r-1}/r$, the maximum of the update function on nonnegative populations.