What is "logistic function"

n. (context mathematics English) A function, the result of the division of two exponential functions, that gives rise to the logistic curve.

A logistic function or logistic curve is a common "S" shape ( sigmoid curve), with equation:

$$f(x) = \frac{L}{1 + \mathrm e^{-k(x-x_0)}}$$

where

• e = the natural logarithm base (also known as Euler's number),
• x = the x-value of the sigmoid's midpoint,
• L = the curve's maximum value, and
• k = the steepness of the curve.

For values of x in the range of real numbers from −∞ to +∞, the S-curve shown on the right is obtained (with the graph of f approaching L as x approaches +∞ and approaching zero as x approaches −∞).

The function was named in 1844–1845 by Pierre François Verhulst, who studied it in relation to population growth. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.

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