Survey of Multistationarity in Reaction Network Theory

The business of Reaction Network Theory is to model and study the dynamical properties of biochemical processes and certain biological systems such ecological dynamics and spread of epidemics. When large number of reactants are present, a system of ODEs, with the dynamical variables representing molecule concentrations, closely approximates the true dynamics. Kinetics is the specification of the concentration-dependent rate at which reactions occur. The most common is mass-action kinetics, for which the reaction rate is proportional to the concentration of the reactants. An important question within mass-action systems is identification of networks which have the property of multistationarity, i.e. networks which have more than one compatible, positive equilibrium. In this thesis, we will present some necessary and sufficient conditions for multistationarity within some biologically relevant networks.