Parametric analysis of dynamically equivalent reaction network models

Abstract

Using the results related to dynamically equivalent realizations of reaction kinetic systems, we analyze the dynamical properties of mass action reaction networks on which the well known structure based theorems of reaction kinetics are not directly applicable with respect to given range of certain rate coefficients. We introduce a transformation matrix to describe parametric changes, and show that if the appropriate transformation matrix has been found, parameter ranges for which certain dynamical properties can be ensured may be determined via the solution of a linear programming problem. The method is illustrated by numerical examples.