(186h) Non-Linear Behavior of Coupled Autocatalytic Reaction Systems

In an autocatalytic reaction one of the products catalyzes its own formation. In this work, we analyze a system consisting of two species, each participating in two autocatalytic reactions. Each species is also responsible for the autocatalytic generation of the other. Such reactions can be used to model systems which show interconversion between two social or religious groups or systems where there is interconversion between two isomers. We analyze how the kinetics of the reaction determines the non-linear behavior of the system such as multiple steady-states. Two cases are considered depending on the kinetics of the two reactions. In the first case both autocatalytic reactions are assumed to be quadratic in nature, while in the second case both autocatalytic reactions are assumed to be 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 this system. Regions in parameter space are identified in the system where a specific kind of bifurcation diagram is obtained. The analysis in this work is focused on determining operating conditions under which a pure enantiomer can be produced from a racemic mixture or one social group completely gets converted to another. The model can also be used to address evolution of species in an eco-system.