Bifurcation analysis: a tool for determining model parameters of the considered process

Abstract

In this paper, we intend to show the importance of the bifurcation analysis in understanding of an oscillatory process. Hence, we use the bifurcation diagram of the Bray–Liebhafsky reaction performed in continuous well-stirred tank reactor under controlled temperature variations for the determination of the activation energies as well as rate constants of particular steps appearing in the kinetic model of oscillatory reaction mechanism. This approach has led us to the development of general procedure for treatment of experimentally obtained data and extracting kinetic parameters from them, which was very important considering that some rate constants of the already proposed model could not be determined experimentally and have to be fitted (or guessed). Also, the proposed approach has the potential to inspire the refinement of already proposed models and the development of a new one that will be able to reproduce experimentally obtained system’s dynamical features more successfully. In particular, the dynamic states of the Bray–Liebhafsky oscillatory reaction have been analyzed experimentally and numerically using already proposed model together with qualitative and quantitative analysis of bifurcation diagrams in both cases.