
CHAPTER 4: Analysis of System Behavior


In this chapter we will take a first short look at what mathematicians have to say about dynamical modeling. In particular, we will set up some simple models in mathematical form (we will meet some old acquaintances), manipulate the equations and solve some of them (Section 4.2), and learn about qualitative methods for discussing system behavior (Section 4.3 through Section 4.5). First, however, we will introduce some solution procedures to get you started on how to find solutions.
CONTENTS
Solving Initial Value Problems 131
Examples of OneDimensional Models 137
The Qualitative Theory of Differential Equations 144
Parameter Dependencies and Bifurcations 149
Two Dimensional Dynamical Systems 153
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