Bifurcation Analysis of an Exothermic Biocatalytic Reaction System

Abstract

This paper focuses on the bifurcation analysis of an exothermic biocatalytic reaction system (EBRS). The objectives of the study were to provide a detailed dynamical systems analysis of an exothermic biocatalytic reaction and examine the long-term behaviours of the system using the techniques from phase portraits and bifurcation analysis. We investigated the combined influences of the proportional control constant and dilution rate on the dynamics of the model. Phase portraits relating to distinct outcomes of EBRS were computed to investigate the existence of different attractors in this system and its stability. Under a fixed dilution rate and different values of proportional control constant, there were four distinct outcomes in our model, which were stable steady states, bistability of two stable steady states, bistability between stable steady states and limit cycle and stable limit cycles. A bifurcation analysis (of codimensions one and two) was performed to examine how the overall dynamics change as chemically relevant parameters were varied. We observed that when the values of proportional control constant were high, the system would achieve stable steady states regardless of how fast the dilution rate was. With lower magnitudes of proportional constant control, bistability occurred and the outcomes of this system depended on the initial conditions. Compared to higher dilution rates scenario, reactions that occurred at lower dilution rates provided higher reaction yields for this EBRS operation; it was also observed that both scenarios produced stable steady-state outcomes with different concentrations. In conclusion, the dynamical system analysis of the model improves our understanding of the EBRS under consideration and these insights may be beneficial for optimising operating conditions of this chemical system.