Parametric Condition for Multistationarity in Biochemical Reaction Networks

Abstract

Chemical Reaction Network theory allows us to decide whether many classes of networks have the capacity for multiple positive equilibria, based on their structural properties. In this way, the deficiency zero theorem asserts that every weakly reversible network of zero deficiency has a unique equilibrium, for any choices of parameter values. We make use of CRNT, aiming not only to discriminate whether a (positive deficiency) network can exhibit multiple steady states, but also to characterize the whole space of the parameters regarding to their capability to produce multistationarity. In this work, we provide a condition, on the parameters of biochemical networks, for the appearance of multistationarity.