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-graphComment: To appear in SIAM Journal on Applied Dynamical System
