Before revision: In this work we extend the characterization of injectivity via the Jacobian criterion first developed by Craciun and Feinberg for chemical reaction networks with outflow reactions to arbitrary chemical reaction networks taken with mass action kinetics . Injective chemical reaction networks do not have the capacity to admit multiple positive steady states for any rate constants and within each stoichiometric class.
After revision: In this work we extend the characterization of injectivity via the Jacobian criterion first developed by Craciun and Feinberg for chemical reaction networks with outflow reactions to arbitrary chemical reaction networks taken with mass-action kinetics to preclude the existence of multiple positive steady states for any rate constants and within each stoichiometric class.