Examples of Global Bifurcation

Abstract

The main goal of this chapter is to give examples of five different types of global bifurcation. While the local bifurcations of the previous chapter were associated with stability changes in an equilibrium, the bifurcations in this chapter are associated with stability changes in a periodic solution. We make no pretense of completeness. It is not remotely possible to classify all possible global bifurcations. We introduce each type of bifurcation with an academic example that may be handled analytically, but for the more interesting examples that follow, we will rely heavily on computations (which we invite you to check) and on intuitive arguments. Even in cases for which proofs are available, we may omit them because we find them unrewarding. Consequently, this chapter is much less dense than the preceding one.