OVERVIEW OF DISCRETE DYNAMICAL MODELING AND MATLAB®
1.1. INTRODUCTION TO MODELING AND DIFFERENCE EQUATIONS
In this section we introduce dynamical systems, discuss discrete dynamical systems vs. continuous dynamical systems and informally define a mathematical model.
1.1.1. Model 1.1: Population Dynamics, A Discrete Dynamical System
Consider the population of a city with a constant growth rate per year. The population is counted at the end of each year. For simplicity, assume that there is no immigration to or emigration from the city.
The relationship between the current population, pn, and the next population, pn+1, is
Therefore, the population dynamics can be modeled by equation ...