Stability analysis of SSN biochemical networks

This paper further investigates the dynamical properties of a class of basic biochemical networks modules - single substrate and single product with no inhibition (SSN) module. It is well known that the biological networks can be modelled by using different kinetics according to their reaction types. This paper introduces the SSN model under the law of mass action and proves that it can admit uniquely globally asymptotically stable positive equilibrium. Moreover, we prove that the SSN module under Hill kinetics can admit uniquely asymptotically stable positive equilibrium. It indicates some potential applications in the understanding of some biological networks modules and the design of some specific network controllers.