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Studies about the set of positive equilibria ($E_+$) of kinetic systems havebeen focused on mass action, and not that much on power law kinetic (PLK)systems, even for PL-RDK systems (PLK systems where two reactions withidentical reactant complexes have the same kinetic order vectors). For massaction, reactions with different reactants have different kinetic order rows. APL-RDK system satisfying this property is called factor span surjective(PL-FSK). In this work, we show that a cycle terminal PL-FSK system with$E_+\ne \varnothing$ and has independent linkage classes (ILC) is a poly-PLPsystem, i.e., $E_+$ is the disjoint union of log-parametrized sets. The keyinsight for the extension is that factor span surjectivity induces anisomorphic digraph structure on the kinetic complexes. The result alsocompletes, for ILC networks, the structural analysis of the original complexbalanced generalized mass action systems (GMAS) by M\"uller and Regensburger.We also identify a large set of PL-RDK systems where non-emptiness of $E_+$ isa necessary and sufficient condition for non-emptiness of each set of positiveequilibria for each linkage class. These results extend those of Boros on massaction systems with ILC. We conclude this paper with two applications of ourresults. Firstly, we consider absolute complex balancing (ACB), i.e., theproperty that each positive equilibrium is complex balanced, in poly-PLPsystems. Finally, we use the new results to study absolute concentrationrobustness (ACR) in these systems. In particular, we obtain a specieshyperplane containment criterion to determine ACR in the system species.

Positive equilibria of power law kinetics on networks with independent linkage classes