We present a unified framework for the preclusion of non-degenerate multiple steady states in a network of interacting species. Interaction networks are modeled via systems of ordinary differential equations in which the form of the species  rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize the set of interaction networks for which any choice of associated rate function is injective within each stoichiometric class and thus  cannot exhibit multistationarity. Our criteria rely on the determinant of the Jacobian of the species rate functions that belong to the class of so-called general mass-action kinetics. The criteria are  computationally tractable and easily implemented. Our approach embraces and extends much previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or non-catalytic kinetics, and also work based on the graphical analysis of the interaction graph associated to the system. 
We present determinant criteria for the preclusion of non-degenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize families of so-called power-law kinetics for which the associated species formation rate function is injective within each stoichiometric class and thus the network cannot exhibit multistationarity. The criterion for power-law kinetics is derived from the determinant of the Jacobian of the species formation rate function. Using this characterization we further derive similar determinant criteria applicable to general sets of kinetics. The criteria are conceptually simple, computationally tractable and easily implemented. Our approach embraces and extends previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or non-catalytic kinetics, and also work based on graphical analysis of the interaction graph associated to the system. Further, we interpret the criteria in terms of circuits in the so-called DSR-graph
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a unified framework
determinant criteria
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a network
networks
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Interaction networks are modeled via systems
A network is modeled as a system
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formation
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the set of interaction networks for which any choice of associated
families of so-called power-law kinetics for which the associated species formation
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the network
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Our criteria rely on
The criterion for power-law kinetics is derived from
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rate functions that belong to the class of so-called general mass-action
formation rate function. Using this characterization we further derive similar determinant criteria applicable to general sets of
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conceptually simple,
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much
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the
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Further, we interpret the criteria in terms of circuits in the so-called DSR-graph