Bifurcation Theory

Aims and Objectives

• To introduce bifurcation theory in the plane.

• To introduce the notion of steady-state solution and investigate multistability and bistability.

• To introduce the theory of normal forms.

On completion of this chapter, the reader should be able to

• describe how a phase portrait changes as a parameter changes;

• plot bifurcation diagrams;

• take transformations to obtain simple normal forms;

• interpret the bifurcation diagrams in terms of physical behavior.