Analysis of the multiple hope bifurcation phenomena in a CSTR with two consecutive reactions—the singlularity theory approach

Abstract

The singularity theory was applied to the analysis of the Hopf bifurcation phenomena by finding multiple Hopf bifurcation points. For a CSTR with two consecutive reactions, two third-order swallow-tail catastrophes were obtained. As the combined results obtained from the static bifurcation of the Hopf bifurcation, it was found that the parameter space could be divided into regions having different numbers of turning points and Hopf bifurcation points. In total 34 bifurcation diagrams were obtained, each of which had different dynamic features and some of which showed the maximum 17 different behaviors of phase plane trajectories for a range of the Damköhler number.