Positive equilibria of power law kinetic systems with kinetics-based decompositions

The goal of this paper is to characterize the existence of positive equilibria of power law systems through their kinetics-based decompositions. To achieve this, we consider subclasses of power law systems: PL-RDK and PL-TIK systems. PL-RDK systems are those in which the kinetic order vectors are reactant-determined, that is, branching reactions have identical vectors. PL-TIK systems are characterized by having linearly independent kinetic order vectors per linkage class. We first introduced the notion of Zero Kinetic Deficiency Decomposition of cycle terminal power law systems. Then, by considering non-cycle terminal power law systems, we extend this by introducing the notion of PL-TIK decomposition. Through these novel decomposition classes, we showed that PL-RDK systems with weakly reversible decompositions admit positive equilibria. Moreover, to ensure the existence of PL-TIK decomposition, we developed an algorithm in which any power law system can generate a PL-TIK decomposition. Lastly, we applied the algorithm to Schmitz’ Global Carbon Cycle Model.