Determination of multiple steady states in an enzyme kinetics involving two substrates in a CSTR

The multiple steady states in an isothermal, constant-density CSTR involving two-substrates, enzyme- catalyzed reactions is determined by a zero eigenvalue analysis. The hysteresis and bistability occurs for a certain range of the rate constant of product formation from a ternary complex, k_ES1S2MP+E. A two-parameter (k_ES1S2MP+E, k_0MS1) bifurcation diagram for several different values of flow rate k_S1̂ is also presented. It shows that, to maintain the existence of the steady state multiplicity under a fixed flow rate, the larger the rate constant k_ES1S2MP+E is, the larger the feed concentration of a substrate is required and the wider the range of that exists. To maintain the existence of the steady state multiplicity for a lower flow rate, it is required to reduce the feed concentration of substrates.