Weakly Reversible CF-Decompositions of Chemical Kinetic Systems

TL;DR

This paper develops new conditions and algorithms for decomposing chemical kinetic systems into weakly reversible CF systems, enabling better analysis of positive equilibria in complex power law systems.

Contribution

It introduces novel criteria and an algorithm for weakly reversible CF-decompositions, extending the analysis of positive equilibria in power law kinetic systems.

Findings

Derived conditions for weakly reversible CF-decompositions.

Presented an algorithm to verify these conditions.

Applied results to determine equilibria in PL-NDK systems.

Abstract

This paper studies chemical kinetic systems which decompose into weakly reversible complex factorizable (CF) systems. Among power law kinetic systems, CF systems (denoted as PL-RDK systems) are those where branching reactions of a reactant complex have identical rows in the kinetic order matrix. Mass action and generalized mass action systems (GMAS) are well-known examples. Schmitz's global carbon cycle model is a previously studied non-complex factorizable (NF) power law system (denoted as PL-NDK). We derive novel conditions for the existence of weakly reversible CF-decompositions and present an algorithm for verifying these conditions. We discuss methods for identifying independent decompositions, i.e., those where the stoichiometric subspaces of the subnetworks form a direct sum, as such decompositions relate positive equilibria sets of the subnetworks to that of the whole network. We then use the results to determine the positive equilibria sets of PL-NDK systems which admit an independent weakly reversible decomposition into PL-RDK systems of PLP type, i.e., the positive equilibria are log-parametrized, which is a broad generalization of a Deficiency Zero Theorem of Fortun et al. (2019).