  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. This result is a
broad generalization of a Deficiency Zero Theorem of Fortun et al. (2019). An
analogous result for complex balanced equilibria of PL-NDK systems is also
derived.
