Dependence on Initial Conditions The behaviors of all dynamic
systems are dependent upon their initial conditions. In
classical mechanics, the initial conditions of systems are
usually known. A very simple example, of a small ball dropped
onto the edge of a razor blade, as shown in Figure 4,
illustrates how important initial conditions can be to a dynamic
system Figure 4. Ball Striking Razor Blade. The ball can strike
the blade in such a way that it can go off to the left (center
of Figure 4) or to the right (right of Figure 4). The initial
condition that will determine whether the ball goes to the left
or right is minute. If the ball were initially held centered
over the blade (left of Figure 4), a prediction of which
direction the ball will bounce would be impossible to make with
certainty. Dynamic systems, that are highly dependent on their
initial conditions, are the main subjects of investigation in
modern chaos theory. Kellert (1993) points out that: “A
dynamical system that exhibits sensitive dependenc