Note: This page is no longer being maintained and is kept for archival purposes only.
For current information see our main page.
Garden with Insight Kurtz-Fernhout Software
Developers of custom software and educational simulations.
Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company
Garden with Insight
Product area
Help System
Quick start

Garden with Insight v1.0 Help: S curve

A typical S curve has an exponential portion in which the slope increases, an inflection point where the slope begins to decrease, and a rounding-off portion where the slope is decreasing. The reason these are called S curves is that they look roughly like an S laid on its side.


S-shaped curves are seen often in nature because they represent a fairly good abstraction of the course of a self-limiting process such as the growth of an organism or population in a limited environment. If two rabbits were placed on an island with no predators but a limited food supply, the number of rabbits would increase exponentially for a time (as long as there was plenty of food), then slow down and finally round off at the carrying capacity of the island -- the number of rabbits the island could accommodate.

This simulation uses S-shaped curves extensively for many processes, including chemical equlibria, plant uptake of nutrients, plant leaf area index (LAI), fruit growth, and soil temperature. Most of the S curves used in this simulation have the form y = x / (x + exp(c1 - c2 * x)) where c1 and c2 are parameters that set the shape of the curve. Depending on these parameters, an S curve can look like the one above, or be reversed, or have an almost imperceptible curve to it. Some other equations use modified versions of this S curve equation.

Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company
Updated: March 10, 1999. Questions/comments on site to
Copyright © 1998, 1999 Paul D. Fernhout & Cynthia F. Kurtz.