ABSTRACT
Chapter 7 presents discrete dynamical systems (DDS). We cover not only simple linear models but nonlinear as well as system of systems. We discuss stability and equilibrium values. Illustrative example include the following: drug dosage, time value of money, simple mortgage, population growth, spread of a contagious disease, inventory systems analysis, competitive hunter model, Lanchester’s combat models, discrete predator–prey model, and a systems model for disease known as the SIR model. We are interested in modeling discrete change. Modeling with DDS employs a method to explain certain discrete behaviors or make long-term predictions. A powerful paradigm that we use to model with DDS is Future value = present value + change https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315150208/4b2c555a-55be-4e37-97d9-dfdf29e1efdd/content/equ7_0000.tif"/>
The dynamical systems that we will study with this paradigm will differ in appearance and composition, but we will be able to solve a large class of these seemingly different dynamical systems with similar methods. In this chapter, we will use iteration and graphical methods to answer questions about the DDS.
