Logistic growth reaction

The logistic growth reaction models the limited growth of a species. It can be used to model auto-catalytic reactions, where the product \(P\) is also the catalyst of the reaction.

\[ \to P \]

The reaction rate for a logistic growth reaction is given by,

\[ r = k\,c\left(1 - \frac{c}{K} \right) \]

Here, \(k\) is the growth rate and \(K\) is the capacity.