Logistic growth curve

From LokDoc

A logistic growth curve is a curve described by the following differential equation. It is usually used to model population growths.

dN/dt = r*N*(1-N/K)

The K is called the carrying capacity. It is the maximum value that is sustainable by the curve and the curve will seek to stabilise at that level. The r is the rate of maximum growth and the N is the parameter value.

Characteristics

A logistic growth curve that starts at a value less than K will slowly start to grow until it reaches a critical N when the curve will start growing at a very fast speed (think population growth). But the curve can't sustain an N higher than K so the growth will slow down and eventually stop when N equals K.

The interesting part is the fast growth but regional growth which is desired in for instance soft-caps. The effect of such a cap is hardly felt until a threshold is reached, then the effect grows very rapidly until it reaches a certain value when it almosts stops. It allows caps that only act on a specific bands of N and that (if desired) never really turn into a hard-caps,

External links

• mathworld: Logistic Equation