11 Facts About Logistic function

Logistic function or logistic curve is a common S-shaped curve with equation.

Logistic function finds applications in a range of fields, including biology, biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks.

Logistic function was introduced in a series of three papers by Pierre Francois Verhulst between 1838 and 1847, who devised it as a model of population growth by adjusting the exponential growth model, under the guidance of Adolphe Quetelet.

Standard logistic function is the solution of the simple first-order non-linear ordinary differential equation.

Qualitative behavior is easily understood in terms of the phase line: the derivative is 0 when the Logistic function is 1; and the derivative is positive for between 0 and 1, and negative for above 1 or less than 0 .

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Logistic function equation is a special case of the Bernoulli differential equation and has the following solution:.

Logistic function is itself the derivative of another proposed activation function, the softplus.

Logistic function determines the statistical distribution of fermions over the energy states of a system in thermal equilibrium.

In linguistics, the logistic function can be used to model language change: an innovation that is at first marginal begins to spread more quickly with time, and then more slowly as it becomes more universally adopted.

Logistic function can be used to illustrate the progress of the diffusion of an innovation through its life cycle.

Logistic function analysis was used in papers by several researchers at the International Institute of Applied Systems Analysis .