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The Deficiency-One Theorem states that there exists a unique positive steadystate in each positive stoichiometric class for weakly reversibledeficiency-one mass action systems with one linkage class (regardless of thevalues of the rate coefficients). The non-emptiness of the set of positivesteady states does not remain valid if we omit the weak reversibility. Arecently published paper provided an equivalent condition to the existence of apositive steady state for deficiency-one mass action systems that are notweakly reversible, but still has only one linkage class. Based on that result,we characterise in this paper those of these mass action systems for which thenon-emptiness of the set of positive steady states holds regardless of thevalues of the rate coefficients. Also, we provide an equivalent condition tothe existence of rate coefficients such that the set of positive steady statesis nonempty for the resulting mass action system.

journal of mathematical chemistry

On the dependence of the existence of the positive steady states on the  rate coefficients for deficiency-one mass action systems: single linkage  class