On the existence of the positive steady states of weakly reversible deficiency-one mass action systems.

In this paper we prove that there exists a positive steady state in each positive stoichiometric class for every weakly reversible deficiency-one mass action system. This qualitative property does not depend on the values of the rate coefficients. Since not all weakly reversible deficiency-one mass action systems satisfy the assumptions of the Deficiency-One Theorem, our result contributes to the theory of deficiency-one mass action systems.

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