Multiplicity, travelling waves and spatial patterns in coupled autocatalytic reaction systems

In an autocatalytic reaction, one of the products catalyzes its own formation. In this work, we analyze a system of two species, each participating in two autocatalytic reactions. Each species participates in the autocatalysis of the other. We first analyze how the kinetics of the reactions determines the non-linear characteristics of the lumped system, such as multiple steady-states. Two cases are considered depending on the kinetics of the two reactions. In the first case, both reactions are quadratic in nature, while in the second, reactions are cubic. Singularity theory and bifurcation theory are employed to comprehensively understand the multiplicity features of the steady states and to classify the bifurcation behavior of the lumped system. The analysis here forms the basis to determine operating conditions under which a pure enantiomer can be produced. The occurrence of spontaneous spatio-temporal features like travelling waves and Turing patterns under specific conditions has been established.