ON THE CREATION, GROWTH AND EXTINCTION OF OSCILLATORY SOLUTIONS FOR A SIMPLE POOLED CHEMICAL REACTION SCHEME.

The equations which govern a simple pooled chemical reaction scheme are analyzed in detail in terms of a nondimensional parameter mu , which represents the amount of the pooled chemical originally present. It is shown that there is one finite equilibrium point, with a Hopf bifurcation occurring at mu equals 1. The phase plane at infinity is then examined and it is shown that there are equilibrium points at infinity at the positive ends of both axes, the nature of which are discussed. This enables the global phase portrait to be constructed for all positive mu . From this it emerges that the stable limit cycle created at mu equals 1 by a Hopf bifurcation is destroyed at mu //0 ( mu //0 less than 1) by an infinite period bifurcation, due to the formation of a heteroclinic orbit by the separatrices from the equilibrium points at infinity. The form of this heteroclinic orbit is then discussed, and it is shown that the value of mu //0 can be determined by simple numerical integration.