Verhulst's logistic curve
| dc.creator | Bradley, David M. | |
| dc.date | 2007-06-21 | |
| dc.date.accessioned | 2026-07-07T08:11:34Z | |
| dc.date.available | 2026-07-07T08:11:34Z | |
| dc.description | We observe that the elementary logistic differential equation dP/dt=(1-P/M)kP may be solved by first changing the variable to R=(M-P)/P. This reduces the logistic differential equation to the simple linear differential equation dR/dt=-kR, which can be solved without using the customary but slightly more elaborate methods applied to the original logistic DE. The resulting solution in terms of R can be converted by simple algebra to the familiar sigmoid expression involving P. A biological argument is given for introducing logistic growth via the simpler DE for R. It is also shown that the sigmoid P may be written in terms of the hyperbolic tangent by a simple translation that is also motivated by a biological argument. | |
| dc.description | 5 pages AMSLaTeX, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0706.3163 | |
| dc.identifier | http://arxiv.org/abs/0706.3163 | |
| dc.identifier | The College Mathematics Journal, Vol. 32, No. 2, March 2001, pp. 94--98. [MR 1833354] (2002c:26002) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132158 | |
| dc.subject | History and Overview | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 26A09; 92D25; 34-01 | |
| dc.title | Verhulst's logistic curve | |
| dc.type | text |