ABSTRACT
A dynamical system is simply a system that changes over time. The bacterial growth model is one such example. When time is measured in discrete increments, such as in the bacterial growth model, the system is called a discrete dynamical system. This chapter introduces basic techniques for formulating dynamical models and graphical approaches to their analysis. It discusses the long–term behavior and equilibria of a discrete dynamical system. A discrete logistic equation (also called a logistic map or a constrained growth model) is often used to model population growth. The chapter describes a linear predator–prey model by considering foxes and rabbits populations in a discrete dynamical system. Each state of the system consists of the populations of foxes and rabbits at a point in time. Since this state consists of two components, this is a two–dimensional discrete dynamical system.
