Chapter 6. S-Shaped Growth

S-shaped growth refers to a general pattern of growth that has been observed in a wide variety of systems. Examples include the growth in certain animal populations (Ricklefs 1990), the spread of epidemics (Hastings 1997), and the diffusion of innovations (Bass 1969; Porter 1980; Sterman [forthcoming]). You've seen the s-shaped pattern in chapter 1, so you know that it begins with a period of exponential growth. You have constructed models to explain exponential growth (appendix C), so you know how to simulate the opening phase of s-shaped growth. You also know that no system can grow forever, so it is useful at this stage to simulate how some systems find a way to slow their growth and arrive at a state of dynamic equilibrium.

This chapter begins with a simple example of the spread of flowers across the landscape. Then, to illustrate the generality of the approach, a second model is constructed to simulate the growth in a sales company. You'll see that the two models generate remarkably similar results. We will attribute the similarity in their dynamic behavior to the similarity in their stock and flow structure. The two models are simple and easy to understand, and they will prove useful again and again throughout the book.