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.