Why
computer modeling?
Why is it necessary to
model these systems with a computer to understand them? Why can't we just
sketch the design of the system with all of the appropriate connections and
leave it at that? As we will see, an intuitive understanding of dynamic systems
is not something we are born with and most people go through their lives
without developing much understanding of how these systems behave. Drawing a
sketch of a system is actually very important since it forces you to think
about relationships, but that sketch is not capable of revealing the dynamics
of the system. That is why we turn to a computer.
Given the prevalence of
these systems and the importance of many of them to our well-being on this planet,
it is very important that more people develop a better sense of these systems,
so we turn to computer modeling for help. Let's look at an example of a system
that appears to be fairly simple and yet turns out to behave in unexpected
ways.
Our example system involves
the populations of hares and lynxes living together in the same region. The
population of either species is simply a function of how many are born and how
many die. The death rate for the hares is dependent on the number of predators
and the likewise, the death rate of the predators is dependent on the number of
hares, assuming that the hares are the only food source for the lynx. So, given
this mutual dependence, how does this system behave? One way to monitor the
behavior of this system is by looking at how the two populations vary through
time. Imagine graphing the histories of these populations - how do you expect
the curves to look? Do you have an intuitive feel for how this system behaves?
If you are like the vast majority of people, the answer is no. As it turns out
(Figure 2.1), the populations oscillate, going up and down with a regular
period, but the peaks and troughs of the two curves are offset slightly. The
hare population peaks out before the lynx population; in a like manner, the
hare population bottoms out slightly before the lynx reach their minimum. In
other words, the two populations oscillate, but they are out of phase - very
complex behavior that is not at all intuitive, yet in reality, their two
populations do behave in this way. The point of this is that even relatively
simple systems are very difficult to really understand - our intuition alone is
not sufficient, and that is why a computer model is useful, in fact, necessary,
to gain a thorough understanding of system dynamics.
Figure
2.1. Oscillating behavior of the Lynx-Hare system. This unexpected behavior
illustrates why computer modeling is necessary to understand the dynamics of
systems. If the Lynx population is altered so that it begins at 1250
individuals rather than 1200, the two populations remain stable. Note that the
vertical scale is different for each species.
The
lynx and hares system has a tendency to oscillate, but there are certain
starting conditions that do not lead to oscillation (see caption to Figure
2.1). It is possible for the two populations to remain stable over time. This
is not something you can grasp unless you are skilled at manipulating
differential equations. But with a computer model of this system, you can learn
these unexpected characteristics of a system by experimenting with it, by changing
the starting conditions around and observing the effects. You will find that
with STELLA, it is quite easy to experiment, to ask
"what if we change this?" and quickly see the results.