Mathematical Modeling and Dynamical Systems

The theory of dynamical systems is applied to problems in many disciplines. Let's take a specific example from biology and environmental science. Consider the population of a particular species of fish in a closed environment such as a pond. How could we model the population from year to year? What factors influence the size of the population? A little thought leads one to realize that food supply and pond size are critical. The art of modeling involves the selection of the simplest model that effectively describes the phenomenon that is observed.