Multistability and sustained oscillations in isothermal, open systems. Cubic autocatalysis and the influence of competitive reactions

The simple, isothermal model of cubic autocatalysis: A+2B→3B, rate = kab² (i), B→C, rate = k_db (ii), exhibits 'exotic' patterns of behaviour, including mushroom and isola dependences of the stationary-state catalyst concentration on residence time and sustained oscillations in well stirred, open systems. In the light of recent criticisms of similar schemes, the effects on these features of various additional steps, reversibility and detailed balance are investigated comprehensively. The two B molecules on the left-hand side of reaction (i) may be regarded as acting as third bodies, providing additional energy. The reactant A may also play such a role. Lower-order catalytic steps and uncatalysed conversions of A and B are also considered, along with multiple conversions such as A + A+(A or B)→B + B+(A or B). Thermodynamic requirements suggest that these additional steps and their reverse should have strictly non-zero (but otherwise quite arbitrary) rate constants. It is shown that all of the above patterns are still found when these extra steps are included, although the range of values of some of these rate constants over which they exist is quite narrow.