Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption