Chaos and Pestilence

Before the advent of modern computer technology and software, many modeling efforts 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 classical mechanics. This science was used to describe the behavior of whole classes of moving objects, such as pendulums, falling rocks, or projectiles. The scientific paradigms 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, welldescribed 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 frequently exhibit characteristics that were previously unanticipated or misidentified.

The emergence of chaos theory made us aware of the importance of nonlinearities, 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 models in Chapter 2—and then in the context of insect dynamics and associated host– parasitoid interactions, which we touch on throughout the book.