Chemical reaction network structure and the stability of complex isothermal reactors—II. Multiple steady states for networks of deficiency one

Abstract

The following problem is considered: Given a deficiency one network, determine whether there exist rate constants for it such that the corresponding isothermal mass action differential equations admit multiple positive steady states. A procedure is given to make this determination for any deficiency one network, no matter how intricate, so long as it satisfies certain weak structural conditions. When there do exist rate constants that give rise to multiple steady states, such rate constants can in fact be exhibited. If multiple steady states are observed in a laboratory reactor with poorly understood chemistry, the theory provides sensitive means to screen candidates for the operative chemical mechanism. Even when measurements of the steady state compositions are fragmentary, the theory will sometimes indicate that a candidate network which does admit multiple steady states will nevertheless be unable to account for the particular measurements made. A catalytic CFSTR is considered as an example.