Stability Analysis for Generalized Butlerov Type Chemical Reaction Network in Batch Reactor

In the present paper, we consider Butlerov type chemical reaction networks (BTCRNs) involving the formation of sugars from formaldehyde. By generalizing BTCRNs based on characteristic network structures of them, we theoretically obtain the productivity of sugars in BTCRNs in the batch reactor. We analyze the ordinary differential equation (ODE) describing the dynamics of concentrations of species in the generalized BTCRNs with a general type of kinetics, and show that any positive solution to the ODE converges to a non-negative equilibrium point, at which the concentrations of formaldehyde and some sugars are zero. This implies that the BTCRNs in the batch reactor cannot obtain various sugars as end-products. From a viewpoint of chemical industry, they have low productivity of sugars at an equilibrium state.