Local Bifurcations

Abstract

In this chapter, we study the local bifurcations of vector fields and maps. As we have seen, systems of physical interest typically have parameters which appear in the defining systems of equations. As these parameters are varied, changes may occur in the qualitative structure of the solutions for certain parameter values. These changes are called bifurcations and the parameter values are called bifurcation values. To the extent possible, we develop in this chapter and Chapters 6 and 7, a systematic theory which describes and permits the analysis of the typical bifurcations one encounters. We pay careful attention to the examples introduced in Chapter 2 and use these to illustrate the theory that we present.