Global bifurcations in a simple, autocatalytic reaction

Abstract

The dynamics of a chemical oscillator based on an autocatalytic reaction are investigated. A simple local stability analysis of the steady states of the system is shown to be insufficient to give a complete picture and, in this case, can be misleading. The bifurcation analysis is therefore extended to search for global bifurcations of limit cycles and homoclinic bifurcations. A recipe for locating and path-following of the homoclinic orbit in parameter space is given. The whole of the parameter plane is thus mapped out, showing all of the local and global bifurcations and the full extent of the oscillatory regions