Related Experiment Video
Updated: Jul 20, 2026
08:55
Visualizing Intracellular SNARE Trafficking by Fluorescence Lifetime Imaging Microscopy
Published on: December 29, 2017
The logistic curve for the fitting of sigmoidal data
Physiological Chemistry and Physics
|January 1, 1981
Summary
The Verhulst differential equation, describing the S-shaped curve, has broad applications. This review highlights its use in population dynamics, physics, chemistry, and biology, demonstrating its versatility.
Area of Science:
- Mathematical Biology
- Population Dynamics
- Applied Mathematics
Background:
- The Verhulst differential equation, developed in 1838, models the S-shaped growth curve.
- This foundational equation has been applied across diverse scientific disciplines.
Purpose of the Study:
- To review the historical application of the Verhulst equation to population data.
- To explore significant later applications in physics, chemistry, and biology.
- To illustrate the equation's utility with examples, including data superimposition using reduced variables.
Main Methods:
- Literature review of the Verhulst differential equation and its applications.
- Analysis of historical population data modeling.
- Case studies demonstrating applications in physics, chemistry, and biology.
Main Results:
- The Verhulst equation effectively models population growth.
- The integrated form of the equation proves useful and versatile across scientific fields.
- Data superimposition via reduced variables is a key application technique.
Conclusions:
- The Verhulst differential equation remains a valuable tool for modeling various phenomena.
- Its adaptability to different scientific domains underscores its significance.
- The integrated equation offers a convenient and powerful analytical approach.
Related Concept Videos
00:57Population Growth
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...
01:20Calibration Curves: Linear Least Squares
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
For data that follow a straight line, the standard method for fitting is the linear...
01:18Survival Curves
Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
01:14Parametric Survival Analysis: Weibull and Exponential Methods
Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
01:23Guidelines for Sketching a Curve
Curve sketching is a systematic method for understanding the overall behavior of a function by analyzing its key mathematical features. A function defines a curve on the coordinate plane, where the horizontal axis represents the input variable and the vertical axis represents the output. The process begins by determining the domain, which specifies the set of input values for which the function is defined and establishes the horizontal extent of the graph.Intercepts with the horizontal and...
01:28Types of Functions III
Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...