Logistic Growth Model - Revision history

Khanh: /* In agriculture: modeling crop response */

2021-10-24T21:46:05Z

In agriculture: modeling crop response

Khanh: /* In agriculture: modeling crop response */

2021-10-24T21:45:13Z

In agriculture: modeling crop response

Khanh at 21:43, 24 October 2021

2021-10-24T21:43:22Z

Show changes

Khanh: Created page with "Standard logistic sigmoid function where $L=1,k=1,x_0=0$ A '''logistic function''' or '''logistic curve''' is a commo..."

2021-09-27T04:20:22Z

Created page with "thumb|320px|right|Standard logistic sigmoid function where <math>L=1,k=1,x_0=0</math> A '''logistic function''' or '''logistic curve''' is a commo..."

New page

[[File:Logistic-curve.svg|thumb|320px|right|Standard logistic sigmoid function where <math>L=1,k=1,x_0=0</math>]]

A '''logistic function''' or '''logistic curve''' is a common S-shaped curve (sigmoid curve) with equation

: <math>f(x) = \frac{L}{1 + e^{-k(x-x_0)}},</math>

where
: <math>x_0</math>, the <math>x</math> value of the sigmoid's midpoint;
: <math>L</math>, the curve's maximum value;
: <math>k</math>, the logistic growth rate or steepness of the curve.

For values of <math>x</math> in the domain of real numbers from <math>-\infty</math> to <math>+\infty</math>, the S-curve shown on the right is obtained, with the graph of <math>f</math> approaching <math>L</math> as <math>x</math> approaches <math>+\infty</math> and approaching zero as <math>x</math> approaches <math>-\infty</math>.

The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I.

==Resources==
* [https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/a/exponential-logistic-growth Exponential and Logistic Growth], Khan Academy

@@ Line 217: / Line 217: @@
 File:Sugarcane S-curve.png|S-curve model for crop yield versus depth of water table.
 File:Barley S-curve.png|Inverted S-curve model for crop yield versus soil salinity.
 === In economics and sociology: diffusion of innovations ===

@@ Line 214: / Line 214: @@
 === In agriculture: modeling crop response ===
 The logistic S-curve can be used for modeling the crop response to changes in growth factors. There are two types of response functions:  ''positive''  and ''negative'' growth curves. For example, the crop yield may ''increase'' with increasing value of the growth factor up to a certain level (positive function), or it may ''decrease'' with increasing growth factor values (negative function owing to a negative growth factor), which situation requires an ''inverted'' S-curve.
-[[File:Sugarcane S-curve.png|S-curve model for crop yield versus depth of water table.]]
+<gallery widths="300">
-[[File:Barley S-curve.png|Inverted S-curve model for crop yield versus soil salinity.]]
+File:Sugarcane S-curve.png|S-curve model for crop yield versus depth of water table.
 === In economics and sociology: diffusion of innovations ===

Logistic Growth Model - Revision history

Khanh: /* In agriculture: modeling crop response */

Khanh: /* In agriculture: modeling crop response */

Khanh at 21:43, 24 October 2021

Khanh: Created page with "Standard logistic sigmoid function where L=1,k=1,x_0=0 A '''logistic function''' or '''logistic curve''' is a commo..."

Khanh: Created page with "Standard logistic sigmoid function where $L=1,k=1,x_0=0$ A '''logistic function''' or '''logistic curve''' is a commo..."