Up: Logistic Growth Model

One-Dimensional Dynamical Systems

Part 2: Logistic Growth Model

Eventual behavior

In order to describe the long term behavior of iterates, we present a few more concepts.

Definition (Fixed Point): The point p is a fixed point of the function f if f(p) = p.

Notice that for the square function, some orbits converge to a point, a fixed point, and some orbits diverge (get arbitrarily large). Are there orbits which always stay bounded, but do not converge to just one point? In general, the answer is yes. You will observe more complicated long term behavior of orbits in your computer investigations.

Definition (Attracting and Repelling Fixed Point): A fixed point p is easy to detect computationally when orbits of nearby points converge to p. In this case, p is called attracting. If the orbits of nearby points move away from p, p is called repelling. If p is neither attracting nor repelling, p is called neutral.

Up: Logistic Growth Model
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Created: Apr 1 1998 --- Last modified: Wed Apr 8 17:58:50 1998