= Logistic growth equation
{title2=$\dot N=rN(1-N/K)$}
The <logistic growth equation> applies the <logistic differential equation> to <population dynamics>. For positive growth rate $r$ and <carrying capacity> $K$, an <initial condition> $0<N(0)<K$ gives $N(t)=K/[1+be^{-rt}]$, where $b=K/N(0)-1$. Its per-capita growth falls linearly with abundance, and a trajectory starting below $K/2$ reaches an <inflection point> when $N=K/2$. The exact <solutions of a differential equation> and their diagrams are developed under <logistic differential equation>. A translated and scaled <logistic function> has the same form. In <nonlinear regression> for biological size, an analogous saturation curve need not imply that circumference itself obeys a mechanistic population law.
Back to article page
