Realization Theory as a Tool of Stability Analysis for Kinetic Systems

Dávid Csercsik and Gábor Szederkényi


Stability, Reaction kinetic systems, Realization theory, Nonnegative systems


The theory of reaction kinetic networks provides powerful theorems about the stability of such systems. It is known however, that different reaction kinetic systems, called realizations, may induce the same differential equations. Since the applicability of stability theorems of chemical reaction network theory depend on the realization structure, for a given dynamics, these theorems might be usable or not depending on the actual realization. In this article we point out that in some cases it may be necessary to determine all possible realizations of the same kinetic system to find one for which an appropriate stability theorem can be applied. Furthermore, we provide an algorithm for the effective calculation of the realizations. We demonstrate the results on simple examples.

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