About Pierre François Verhulst
Pierre François Verhulst (28 October 1804, in Brussels – 15 February 1849, in Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model. == Biography == Pierre François Verhulst was born in the French Empire, now Brussels. His family was a wealthy family, being able to give him a high-quality education and promoting his later career. He could obtain his doctorate on August 3rd in 1825. == Logistic equation == Verhulst developed the logistic function in a series of three papers between 1838 and 1847, based on research on modeling population growth that he conducted in the mid-1830s, under the guidance of Adolphe Quetelet; see Logistic function § History for details. Verhulst published in Verhulst (1838) the equation: d N d t = r N − α N 2 {\displaystyle {\frac {dN}{dt}}=rN-\alpha N^{2}} where N(t) represents number of individuals at time t, r the intrinsic growth rate, and α {\displaystyle \alpha } is the density-dependent crowding effect (also known as intraspecific competition). In this equation, the population equilibrium (sometimes referred to as the carrying capacity, K), N ∗ {\displaystyle N^{*}}, is N ∗ = r α {\displaystyle N^{*}={\frac {r}{\alpha }}}. In Verhulst (1845) he named the solution the logistic curve. Later, Raymond Pearl and Lowell Reed popularized the equation, but with a presumed equilibrium, K, as d N d t = r N ( 1 − N K ) {\displaystyle {\frac {dN}{dt}}=rN\left(1-{\frac {N}{K}}\right)} where K sometimes represents the maximum number of individuals that the environment can support.
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