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Abstract

This paper addresses the problem of determining the capacity of a deficiency-one network, endowed with rate laws more general than mass action kinetics, to admit multiple positive steady statesthat is, whether there exist rate constants such that the corresponding differential equations admit two distinct stoichiometrically compatible steady states where all concentrations are positive. We extend the Deficiency-One Algorithm of M. Feinberg to deal with PL-RDK systems, which are kinetic systems with power-law rate functions whose kinetic orders are identical for reactions with the same reactant complex. The algorithm is applied to a power-law approximation of the Earth's pre-industrial carbon cycle model, which gave the original motivation for our study.