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We show that weakly reversible mass-action systems can have a continuum ofpositive steady states, coming from the zeroes of a multivariate polynomial.Moreover, the same is true of systems whose underlying reaction network isreversible and has a single connected component. In our construction, we relateoperations on the reaction network to the multivariate polynomial occurring asa common factor in the system of differential equations.

Weakly reversible mass-action systems with infinitely many positive steady states