Logistic equation parameters

Logistic function is used for e.g. firmness simulations in “Peaple”. It may be described by different equations, one of them is the following:

Each logistic equation has three characteristic parameters – upper asymptote (Fmax in above equation), bottom asymptote (Fmin in above equation) and kinetic parameter (ka in above equation). There is one more parameter in each logistic equation – parameter related to the value 0 at X axis. Since in case of firmness simulation the X axis is the time “t” axis, the 0 value is usually at the start of known firmness changes. The firmness level at that time point is described by F0 parameter in the above equation.

The upper and bottom asymptotes are the mathematical limits for planned simulation. It means that e.g. the initial firmness cannot be higher than upper asymptote, and the software will display an error message (or red dot) in case of such attempt.

The kinetic rate defines the time required for simulated quality index before it will reach the vicinity of its final asymptote.