Ricker population map
= Ricker population map
{c}
{title2=$N_{t+1}=N_t e^{r(1-N_t/K)}$}
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.