A logistic function or logistic curve 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. As shown below, the untrammeled growth can be modelled as a rate term +rKP (a percentage of P). But then, as the population grows, some members of P (modelled as −rP2) interfere with each other in competition for some critical resource (which can be called the bottleneck, modelled by K). This competition diminishes the growth rate, until the set P ceases to grow (this is called maturity).
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An S-shaped (sigmoid) function having values in the range (0,1). See, the Logistic Distribution.
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