Complex Balanced Equilibria of Weakly Reversible Power Law Kinetic Systems

In this paper, we use the concept of kinetic reactant deficiency to determine the existence of complex balanced equilibria of power law kinetic systems. We previously introduced a class of power law kinetic systems whose kinetic order vectors (which we call "interactions") are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class, denoted by PL-TIK systems. A subset of PL-TIK systems was found to admit a complex balanced equilibrium. In this work, we prove that zero kinetic reactant deficiency systems are precisely the PL-TIK systems. Our main result is the existence of complex balanced equilibria for weakly reversible systems with zero kinetic reactant deficiency (for any rate constant), hence, generalizing the previous study