Abstract
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.
Highlights
Chemical Reaction Networks (CRNs) form a wide class of positive systems attracting significant attention among chemists but in numerous other fields such as physics, or Entropy 2010, 12 even pure and applied mathematics where nonlinear dynamical systems are considered [1]
The thermodynamic approach recognizes, that the reaction kinetic equations originate from dynamic conservation balances constructed for component masses, and utilizes the second law of thermodynamics [10] to associate an entropy-based Lyapunov function candidate to investigate the stability of the system
Lyapunov function candidate serves as a tool for proving structural stability for closed reaction kinetic system obeying the Mass action law (MAL)
Summary
Chemical Reaction Networks (CRNs) form a wide class of positive (or non-negative) systems attracting significant attention among chemists but in numerous other fields such as physics, or Entropy 2010, 12 even pure and applied mathematics where nonlinear dynamical systems are considered [1]. The dimension of the stoichiometric space remains s = 3, the reduced model is of zero deficiency, and it is structurally stable For both the quasi equilibrium and quasi steady state assumptions, the underlying physical picture determines the conditions under which it can be applied. It is important to note, that the reaction kinetic form may be, and in most of the cases will be, destroyed when one eliminates one of the concentration variables by expressing it from the algebraic equations, and substitutes the resulting expression into the differential ones This substitution will be circumvented here by choosing carefully the model reduction transformation. Model reduction using two quasi steady state assumptions is presented
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