The logistic equation (sometimes called the Verhulst model or logistic growth curve) is a
model of population growth first published by Pierre-Fran¸cois Verhulst (1845,1847). The
model is continuous in time, but a modification of the continuous equation to a discrete
quadratic recurrence equation, known as the logistic map, is also widely studied.
The continuous version of the logistic model is described by the differential equation: