Logistic functions :

When we started to model biological behaviors, we realised very soon that we were going to need a function that simulates a non-exponential evolution, that would include a simple speed control and a maximum value.

Such functions, named logistic functions were introduced around 1840 by M. Verhulst.

These functions looked perfect, but we needed more control : we needed to set a starting value and a precision. The addition of the parameters d and p allowed us to directly control these crucial informations : f(d)=p.