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Mass action systems capture chemical reaction networks in homogeneous anddilute solutions. We suggest a notion of generalized mass action systems thatadmits arbitrary nonnegative power-law rate functions and serves as a morerealistic model for reaction networks in intracellular environments. Inaddition to the chemical complexes and the related stoichiometric subspace, weintroduce corresponding kinetic complexes, which represent the nonnegativeexponents in the rate functions and determine the kinetic-order subspace. Weshow that several results of Chemical Reaction Network Theory carry over to thecase of generalized mass action kinetics. Our main result essentially statesthat, if the sign vectors of the stoichiometric and the kinetic-order subspacecoincide, there exists a unique positive complex balancing equilibrium in everystoichiometric compatibility class. However, in contrast to classical massaction systems, multiple complex balancing equilibria in one stoichiometriccompatibility class are possible in general.

Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces