MATHEMATICAL-ANALYSIS OF THE SMALLEST CHEMICAL-REACTION SYSTEM WITH HOPF-BIFURCATION

Recently we presented an up to now unstudied three-dimensional dynamic al system which is, according to our given definition, the smallest ch emical reaction system with Hopf bifurcation. We here study the Hopf b ifurcation in detail and prove that near the bifurcation point a stabl e limit cycle arises. In the analysis we use the methods of local bifu rcation theory, especially the center manifold and the normal form the orem. In a similar way we analyse the also occurring transcritical bif urcation. Besides studying local stability, we give the proofs for glo bal stability of the trivial steady state in the whole positive phase space and for the nontrivial steady state in a closed domain containin g the steady state point.