ABSTRACT
This chapter describes the beautiful mathematical subject known as dynamical systems theory. There are many mathematical models to predict the behavior of populations. By far the simplest (and most naive) is the exponential growth model. Differential equations are also examples of dynamical systems. Unlike iterative processes where time is measured in discrete intervals such as years or generations, differential equations are examples of continuous dynamical systems wherein time is a continuous variable. Ever since the time of Newton, these types of systems have been of paramount importance. However, discrete dynamical systems have also received considerable attention. This does not mean that continuous systems have declined in importance. Rather, mathematicians study discrete systems with an eye toward applying their results to the more difficult continuous case. There are a number of ways that iterative processes enter the arena of differential equations.
