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Chapter 13
Chaos and Pestilence
Before the advent of modern computer technology and software, many modeling ef-
forts and scientific experiments were designed for linear, often static systems, which
had the advantage of being analytically solvable. The ways of thinking about system
behavior and the tools applied to describe that behavior was rooted deeply in clas-
sical mechanics. This science was used to describe the behavior of whole classes of
moving objects, such as pendulums, falling rocks, or projectiles. The scientific par-
adigms associated with classical mechanics were not only applied in the realm of
the natural sciences but increasingly influenced models of economic and ecological
systems as well.
The strength of these paradigms lies in their view of systems as predictable, well-
described entities that can be analyzed with available mathematical tools. Students
were told that nonlinear systems are generally unsolvable and that such systems are
exceptions. The first of these statements is true; nonlinear systems, some of which
we modeled in the previous chapters, generally do not have an explicit mathematical
solution. However, the second statement, that nonlinear systems are exceptions, is
false. Rather, many real systems are governed by nonlinearities. These systems fre-
quently exhibit characteristics that were previously unanticipated or misidentified.
The emergence of chaos theory made us aware of the importance of nonlinear-
ities, a lack of predictability that is inherent in many of these nonlinear systems,
the sensitivity of model results to small changes in initial conditions, and therefore,
the need for increased computer modeling efforts. Today, chaos theory begins to
influence thinking in modern natural sciences as well as in the social sciences. In
the following sections of this chapter, we develop models with potentially chaotic
behavior first in the context of the spread of a disease—akin to the simple mod-
els in Chapter 2—and then in the context of insect dynamics and associated host-
parasitoid interactions, which we touch on throughout the topic.
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