Global Dynamics of the smallest Chemical Reaction System with Hopf Bifurcation

Details Global Dynamics of the smallest Chemical Reaction System with Hopf Bifurcation Global Dynamics of the smallest Chemical Reaction System with Hopf Bifurcation

2011-09-23

arxiv.org/abs/1109.5204v1

Mathematics

Dynamical Systems

Scientific paper

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}.

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