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In this paper we discuss the question of how to decide when a generalchemical reaction system is incapable of admitting multiple equilibria,regardless of parameter values such as reaction rate constants, and regardlessof the type of chemical kinetics, such as mass-action kinetics,Michaelis-Menten kinetics, etc. Our results relate previously described linearalgebraic and graph-theoretic conditions for injectivity of chemical reactionsystems. After developing a translation between the two formalisms, we showthat a graph-theoretic test developed earlier in the context of systems withmass action kinetics, can be applied to reaction systems with arbitrarykinetics. The test, which is easy to implement algorithmically, and can oftenbe decided without the need for any computation, rules out the possibility ofmultiple equilibria for the systems in question.

Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems