Complex bifurcations in the oscillatory reaction model

Abstract

The mixing of different types of bifurcations, i.e. supercritical Andronov-Hopf (SAH), double loop (DL) and saddle-loop (SL) bifurcations in the vicinity of their total annihilation, is examined on the highly nonlinear six-variable model for the Bray-Liebhafsky (BL) oscillatory reaction under continuously well-stirred tank reactor (CSTR) conditions. For this kind of the reaction system where the law of mass conservation is additional constraint that must be satisfied and where because of that, some simple bifurcations cannot be formed independently to the others, the considered transformations of the bifurcations are particularly important. That is why as the control parameters for bifurcation analysis, the specific flow rate (j0), as well as the inflow hydrogen peroxide concentration (h = [H2O2]in), were used. The complex bifurcations obtained from numerical simulations are compared with some experimental results. It was shown that these complex bifurcations cannot be easily recognized in experimental investigations without knowing their evolution.