Stability of Rate-Controlled Zero-Deficiency Networks

Zero deficiency networks describe a class of biochemical reaction networks which follow the law of mass-action kinetics, and are modeled by a system of differential equations with polynomial vector fields, and constant reaction rate parameters. In this paper, the parameters are regarded as time-variant inputs, and an input-to-state stability property is established for the system. The biochemical networks can thus be analyzed for robustness with respect to perturbations in their nominal parameters, or stability in the case of reaction rates controlled by an independent dynamical process