Notice sur la loi que la population suit dans son accroissement¶
Verhulst, P. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondance Mathématique et Physique.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Amara's Law
- Let cumulative impact follow the S-shaped realization curve $f(t) = L / (1 + e^{-k(t - t_0)})$, with low early slope, a steep middle, and a saturating plateau at $L$.
This sourceOrigin of the logistic growth curve f(t)=L/(1+e^{-k(t-t0)}) used as the S-shaped realization curve.
- Let cumulative impact follow the S-shaped realization curve $f(t) = L / (1 + e^{-k(t - t_0)})$, with low early slope, a steep middle, and a saturating plateau at $L$.
- Carrying Capacity
- A population N grows according to dN/dt = rN(1 − N/K), where r is the intrinsic growth rate and K is the carrying capacity.
This sourceIntroduces the logistic growth equation dN/dt = rN(1 − N/K) with K as the carrying capacity. (Link is Bacaër's annotated reproduction and translation of the original memoir.)
- A population N grows according to dN/dt = rN(1 − N/K), where r is the intrinsic growth rate and K is the carrying capacity.
- Logistic Growth
- In population biology and ecology, the Verhulst-Pearl equation for a population growing into a fixed-resource environment is the original substrate, with the S-curve falling out of births proportional to current population and deaths rising with density.
This sourceOriginal derivation of the logistic equation dN/dt = rN(1 − N/K) for population growing against a finite ceiling, with its sigmoid solution, fixed points, and half-ceiling inflection. (Reproduced and analyzed in Bacaër 2011, ch. 6: https://doi.org/10.1007/978-0-85729-115-8_6)
- In population biology and ecology, the Verhulst-Pearl equation for a population growing into a fixed-resource environment is the original substrate, with the S-curve falling out of births proportional to current population and deaths rising with density.
- Nonlinearity
- … strain, the Belousov-Zhabotinsky and other chemical oscillators, fluid turbulence (the convective term in the Navier-Stokes equations is the canonical fluid nonlinearity), and Einstein's nonlinear field equations of general relativity. Biology and ecology uses nonlinearity for logistic population growth (Verhulst
This source(Originating treatment of the logistic equation `dN/dt = rN(1 − N/K)` for population growth with a carrying-capacity saturation; founding instance of saturation nonlinearity in dynamical modelling.)
- … strain, the Belousov-Zhabotinsky and other chemical oscillators, fluid turbulence (the convective term in the Navier-Stokes equations is the canonical fluid nonlinearity), and Einstein's nonlinear field equations of general relativity. Biology and ecology uses nonlinearity for logistic population growth (Verhulst
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