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Logistic growth never is negative, but in the saturation area, the growth is as small as before the market took off. (In the example all curves are scaled to cover the range between 0 and 1.) In economics, market saturation is a situation in which a product has become diffused (distributed) within a market; [1] the actual level of saturation ...
Lyapunov exponent. In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector diverge (provided that the divergence can be treated ...
Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. [2] The global population has grown from 1 billion in 1800 to 7.9 billion in 2020. [3] The UN projected population to keep growing, and estimates have put ...
Logistic equation can refer to: Logistic map, a nonlinear recurrence relation that plays a prominent role in chaos theory. Logistic regression, a regression technique that transforms the dependent variable using the logistic function. Logistic differential equation, a differential equation for population dynamics proposed by Pierre François ...
The term generalized logistic distribution is used as the name for several different families of probability distributions. For example, Johnson et al. [1] list four forms, which are listed below. Type I has also been called the skew-logistic distribution. Type IV subsumes the other types and is obtained when applying the logit transform to ...
The Bass model or Bass diffusion model was developed by Frank Bass. It consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact. The basic premise of the model is that adopters can ...
A logistic function or logistic curve is the most common sigmoid curve. It models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops. A logistic function is defined by the mathematical formula:
In an equation of the form y' = f ( x , y ), the isoclines are lines in the ( x , y) plane obtained by setting f ( x , y) equal to a constant. This gives a series of lines (for different constants) along which the solution curves have the same gradient. By calculating this gradient for each isocline, the slope field can be visualised; making it ...