Global Dynamics of the smallest Chemical Reaction System with Hopf Bifurcation

The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in \cite{WH1}. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincar'e-Bendixson theory extends to such systems \cite{MS,H0,HS,S} and a Bendixson criterion exists to rule out periodic orbits \cite{LM}.