TITLE: Why is logistic equation called "logistic"?
QUESTION [31 upvotes]: The logistic function solves the logistic ODE which is the continuous version of the logistic map.
However, I was not able to find why any of these things are called "logistic".

REPLY [6 votes]: (Cross-posted from History of Science and Mathematics: source of “logistic growth”?)
As stated above, the term logistic is due to the Belgian mathematician Pierre François Verhulst, who invented the logistic growth model, and named it logistic (French: logistique) in his 1845 "Recherches mathématiques sur la loi d'accroissement de la population", p. 8:

Nous donnerons le nom de logistique à la courbe

We will give the name logistic to the curve


He does not explain why he uses this term, but it is presumably by analogy with arithmetic and geometric, and in contrast to logarithmic, as in figure below (from the original paper).
The French term logistique is from Ancient Greek λογιστικός (logistikós, “practiced in arithmetic; rational”), from λογίζομαι (logízomai, “I reason, I calculate”), from λόγος (lógos, “reason, computation”), whence English logos, logic, logarithm, etc. In Ancient Greek mathematics, logistikós was a division of mathematics: practical computation and accounting, in contrast to ἀριθμητική (arithmētikḗ), the theoretical or philosophical study of numbers. Confusingly, today we call practical computation arithmetic, and don't use logistic to refer to computation.
Verhulst first discusses the arithmetic growth and geometric growth models, referring to arithmetic progression and geometric progression, and calling the geometric growth curve a logarithmic curve (confusingly, the modern term is instead exponential curve, which is the inverse), then follows with his new model of "logistic" growth, which is presumably named by analogy, after a traditional division of mathematics, and in contrast to the logarithmic curve. The term logarithm is itself derived as log-arithm, from Ancient Greek λόγος (lógos) and ἀριθμός (arithmós), the sources respectively of logistic and arithmetic.
There is no connection with logistics (1830), which is instead from logis (lodging), and was military jargon.