Pierre-francois verhulst biography

Pierre-francois verhulst biography: Pierre François Verhulst was a Belgian

He is best known for the logistic growth model. In Verhulst he named the solution the logistic curve. Later, Raymond Pearl and Lowell Reed popularized the equation, but with a presumed equilibrium, Kas. The Pearl-Reed logistic equation can be integrated exactly, and has solution. The solution can also be written as a weighted harmonic mean of the initial condition and the carrying capacity.

Although the continuous-time logistic equation is often compared to the logistic map because of similarity of form, it is actually more closely related to the Beverton—Holt model of fisheries recruitment. Contents move to sidebar hide. In [ 13 ] Quetelet says that Verhulst took the utmost care with the preparation of his lecture notes for his courses at the Military Academy, and continually updated and improved them.

There he gave courses on astronomy, celestial mechanics, the differential and integral calculus, the theory of probability, geometry and trigonometry.

Pierre-francois verhulst biography: Pierre François Verhulst (28 October

He continued to be influenced by Quetelet although he was not always in agreement with Quetelet 's ideas. However, one project by Verhulst which Quetelet praised highly was his work on elliptic functions. This came about since Verhulst bought an edition of the complete works of Legendre in a public sale. Quetelet praised the work highly and it must have been a contributory factor in Verhulst's election to the Belgium Academy of Science later in Quetelet does not seem to have appreciated Verhulst's most important contribution, however, namely his work on the logistic equation and logistic function.

The assumed belief before Quetelet and Verhulst worked on population growth was that an increasing population followed a geometric progression. Quetelet believed that there are forces which tend to prevent this population growth and that they increase with the square of the rate at which the population grows. Verhulst wrote in his paper:- We know that the famous Malthus showed the principle that the human population tends to grow in a geometric progression so as to double after a certain period of time, for example every twenty five years.

This proposition is beyond dispute if abstraction is made of the increasing difficulty to find food The virtual increase of the population is therefore limited by the size and the fertility of the country. As a result the population gets closer and closer to a steady state. In the paper Verhulst argued against the model for population growth that Quetelet had proposed and instead proposed a model with a differential equation now known as the logistic equation.

He named the solution to the equation he had proposed in his paper the 'logistic function'. It is unclear why he gave it this name and in [ 12 ] Hugo Pastijn considers certain possible explanations:- The reason why Verhulst called this curve "a courbe logistique" in his communication of November 30, is not clear. He does not give any explanation.

One might guess that he refers to the term logistics, related to transportation and distribution in the supply chain of an army, analogous to the supply of subsistence means of a population which he considered to be limited. The term pierre-francois verhulst biography was then already to a certain extent in use in the military environment. He could have been familiar with it, through his military contacts in the Military Academy in Brussels.

Another pierre-francois verhulst biography root of the term logistic could have been the French word "logis" place to live which was of course related to the limited resources for subsistence of a population, Verhulst was dealing with in his model. In this paper, which was published inVerhulst writes:- We shall not insist on the hypothesis of geometric progression, given that it can hold only in very special circumstances; for example, when a fertile territory of almost unlimited size happens to be inhabited by people with an advanced civilization, as was the case for the first American colonies.

He showed that forces which tend to prevent a population growth grow in proportion to the ratio of the excess population to the total population. Verhulst checked his theory empirically against population data for France, Belgium, Essex, England, and Russia. Quetelet, however, was not convinced by his student since he knew of no counterpart in physics.

After the publication of Verhulst's theory, the logistic curve was forgotten until its rediscovery by the American biometrician Raymond Pearl and demographer Lowell J. Reed inand British statistician G. Udny Yule's acknowledgment of the significance of Verhulst's finding of almost a century earlier. From the s onward, many applications for the theory were found in a wide variety of fields.

The logistic curve became one of the essential cornerstones of world systems modeling. It also proved to provide good descriptions of certain diffusion processes, especially of those based on the principles of contagion. Diseases, technical novelties, new ideas and rumors would all grow within a virgin population and reach a maximum, but each would eventually encounter resistance and burn out, or be challenged by a better invention or concept.

In the field of mathematics, Verhulst's logistic curve was rediscovered in by two German physicists who determined that it was one of the essential formulas in the mathematics of fractals. In the early twenty-first century, Quetelet's contributions to demography have largely faded, while those of Verhulst have steadily increased in importance.

However, he is still rarely cited by demographers as the inventor of the logistic curve or the contagion model of diffusion. Kint, Jos. Cite this article Pick a style below, and copy the text for your bibliography. In Quetelet was assigned the task of drawing up mortality tables for the new Belgium State and he asked Verhulst to assist him in this.

Pierre-francois verhulst biography: On 28 September Verhulst was

However, one project by Verhulst which Quetelet praised highly was his work on elliptic functions. This came about since Verhulst bought an edition of the complete works of Legendre in a public sale. Quetelet praised the work highly and it must have been a contributory factor in Verhulst's election to the Belgium Academy of Science later in Quetelet does not seem to have appreciated Verhulst's most important contribution, however, namely his work on the logistic equation and logistic function.