Abstract
In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population. He used data from several countries, in particular Belgium, to estimate the unknown parameters. The work of Verhulst was rediscovered only in the 1920s.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Further reading
Lloyd, P.J.: American, German and British antecedents to Pearl and Reed’s logistic curve. Pop. Stud. 21, 99–108 (1967)
McKendrick, A.G., Kesava Pai, M.: The rate of multiplication of micro-organisms: A mathematical study. Proc. R. Soc. Edinb. 31, 649–655 (1911)
Pearl, R.: The Biology of Death. Lippincott, Philadelphia (1922). www.archive.org
Pearl, R., Reed, L.J.: On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Natl. Acad. Sci. 6, 275–288 (1920). www.pnas.org
Quetelet, A.: Sur l’homme et le développement de ses facultés. Bachelier, Paris (1835). gallica.bnf.fr
Quetelet, A.: Pierre-François Verhulst. Annu. Acad. R. Sci. Lett. B.-Arts Belg. 16, 97–124 (1850). books.google.com
Quetelet, A.: Sciences mathématiques et physiques au commencement du xix ième siècle. Mucquardt, Bruxelles (1867). gallica.bnf.fr
Robertson, T.B.: On the normal rate of growth of an individual and its biochemical significance. Arch. Entwicklungsmechanik Org. 25, 581–614 (1908)
Verhulst, P.-F.: Notice sur la loi que la population poursuit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838). books.google.com
Verhulst, P.-F.: Recherches mathématiques sur la loi d’accroissement de la population. Nouv. Mém. Acad. R. Sci. B.-lett. Brux. 18, 1–45 (1845). gdz.sub.uni-goettingen.de
Verhulst, P.-F.: Deuxième mémoire sur la loi d’accroissement de la population. Mém. Acad. R. Sci. Lett. B.-Arts Belg. 20, 142–173 (1847). www.digizeit-schriften.de
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Bacaër, N. (2011). Verhulst and the logistic equation (1838). In: A Short History of Mathematical Population Dynamics. Springer, London. https://doi.org/10.1007/978-0-85729-115-8_6
Download citation
DOI: https://doi.org/10.1007/978-0-85729-115-8_6
Publisher Name: Springer, London
Print ISBN: 978-0-85729-114-1
Online ISBN: 978-0-85729-115-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)