ABSTRACT
This chapter describes four different examples of dynamical systems that arise in practice. 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. Recently, 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. Most often, differential equations are impossible to solve explicitly. People must turn to the computer to generate numerical solutions. The numerical methods used to solve these equations are often iterative processes such as the Runge-Kutta method.
