Growth law
Growth laws or growth models have been known in science since Thomas Robert Malthus compared the geometric sequence as a model for population growth to the linear growth of resources in 1798. A model that captures the actual conditions more appropriately is the logistic model developed by Pierre-François Verhulst (1838, 1845) (see logistic equation ), which shows growth in the form: slow beginning - ever increasing growth - turning point - gradual declining growth - describes the end of growth. Decay processes also follow this model - when a sign changes . In the term logistically infected French. Logis for habitat . In addition to the geometric and logistic models, there are a few other growth models.
Such growth models play a role in many sciences, including a. as language change laws and language acquisition laws in linguistics, especially in quantitative linguistics , when depicting the course of language change and language acquisition processes.
Another example of the application of the logistic model can be found in communications research, where it depicts the propagation of messages from person to person. However, the applications of growth models in the bio and economic sciences are better known.
literature
- Robert B. Banks: Growth and Diffusion Phenomena. Mathematical Frameworks and Applications. Springer, Berlin a. a. 1994. ISBN 3-540-55507-2
- Karl-Heinz Best , Jörg Kohlhase (Ed.): Exact language change research. Theoretical contributions, statistical analyzes and work reports . edition herodot, Göttingen: 1983. ISBN 3-88694-024-1
- Karl-Heinz Best, Jinyang Zhu: Language change in Chinese. In: Archív Orientální 74, 2006, 203-214.
- Stuart C. Dodd: Testing Message Diffusion from Person to Person. In: Public Opinion Quarterly XVI, 1952, 247-262.
- Thomas Robert Malthus : An Essay on the Principle of Population as it Affects the Future Improvement of Society, with Remarks on the Speculations of Mr. Godwin, M. Condorcet, and Other Writers. London 1798. Dt. Translation: The Population Law. Deutscher Taschenbuchverlag, Munich 1977. ISBN 3-423-06021-2
- Louis Perridon , Manfred Steiner : Finance of the company. 11., revised. u. exp. Ed. Vahlen, Munich 2002. ISBN 3-8006-2796-5
- Rainer Schimming: Differential equations in the life sciences. Scripts for a lecture given in the 1998 summer semester. Ernst Moritz Arndt University of Greifswald, Institute for Mathematics and Computer Science.
- Pierre-François Verhulst : Notice sur la loi que la population suit dans son accroissement. In: Correspondance Mathématique et Physique , Tome X, 1838, 3-21.
- Pierre-François Verhulst: Recherches mathématiques sur la loi d'accroissement de la population. In: Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles , Tome XVIII, 1845, 5-38.
- Rüdiger Wehner , Walter Gehring : Zoology. 22nd, completely revised edition. Thieme, Stuttgart / New York 1990. ISBN 3-13-367422-6