Bifurcation analysis of the reduced model of the Bray–Liebhafsky reaction

Abstract

In this paper, an already published model of the Bray–Liebhafsky reaction was improved by removing the direct autoinhibitory step, which resulted in a new variant of the model with more realistic kinetic scheme than the earlier version. The obtained variant of the model retains all intermediate species (I−, HIO, HIO2 and I2) that were present in the previous model and has one reaction less. Stability analysis of the improved model was performed by stoichiometric network analysis (SNA). By this method, it was shown that improved model can simulate Andronov–Hopf and saddle-node bifurcations. In order to confirm the results of SNA, bifurcation analysis was performed with the initial concentrations of [H2O2]0 as the control parameter. With selected set of rate constants and constant concentrations of external species, two Andronov–Hopf bifurcations were detected at [H2O2]0 = 5.62 × 10−2 M and [H2O2]0 = 10.73 M, while the rate constants ought to be changed for a saddle-node to occur. Bifurcation analysis also showed that the interaction between intermediate species I–, HIO and HIO2 has a crucial impact on the emergence of Andronov–Hopf bifurcation.