A simple model for Hopf bifurcations and other transition phenomena in isothermal, homogeneous and open chemical systems

Abstract

A simple bimolecular reaction model A + B → C + D, B + C → 2B, B → P which (both reversible and irreversible versions) exhibits Hopf bifurcation phenomena and other complex dynamical behaviour under isothermal, homogeneous and open (CSTR) conditions has been proposed. It is shown that there may exist at most three Hopf bifurcation points on the same stationary-state branch of the one-parameter (flow-rate) bifurcation diagram. For certain values of the second parameter, two Hopf bifurcation points may coalesce and two sets of oscillatory branches bifurcate from such a coalescent bifurcation point; at the same time a region of stable stationary states disappears.