A new, powerful mathematical technique enables a systematic determination of the maximal number of steady-state solutions of lumped parameter systems in which complex enzymatic reaction occur. The method can predict also the different types of diagrams describing the dependence of a state variable of the reactor on a design or operating variables.
The system analyzed is a CSTR in which an enzymatic reaction occur, whose mechanism is that an enzyme catalyze two substrates sequentially and then form a products. The value of bifurcation parameter changes by varying the total enzyme concentration or dilution rate. The state variable is a conversion of substrate A.
Multiple steady-states exhibits as the types of hysteresis and double limit. When the derivatives of steady-state equation with respect to the bifurcation parameter does not vanish, it is obtained one cusp and one ray in parameter space which corresponds with the hysteresis and double limit points, respectively. Also, when the derivatives with respect to the bifurcation parameter vanish, there exists hysteresis and double limit points. And all the possible inequivalent bifurcation diagrams are obtained.
