ABSTRACT
Ordinary differential equations arise in many ways in the study of nonlinear dynamics, including nonlinear optics. Typically such equations may arise in systems near to one or other physical limit. Sometimes they arise when looking for particular kinds of solution to a partial differential equation, such as travelling wave solutions. In other cases it may be appropriate to look at ordinary differential equations which provide good models for the behaviour near one or other kind of bifurcation occurring in a more general system. Whatever ones original motivation, it often becomes necessary to understand the behaviour of an ordinary differential equation in some detail. The purpose of these lectures is to look at one particular aspect of the behaviour of nonlinear ordinary differential equations, and I shall approach this problem directly without being concerned with the derivation of the equation or original motivation for its study. In particular, as the title suggests, we shall be looking at certain global bifurcations which can occur in these systems.
