Stability analysis of chemical reaction networks by decomposing them into weakly reversible sub-networks

The chemical reaction network theory, which has been established by M. Feinberg and his collegues, gives an important theorem called the Deficiency Zero Theorem (DZT). This theorem provides methods for analyzing the stability of ODEs that describe the time-evolutions of molar concentrations of species in chemical reaction networks. In the present paper, we consider a class of non-weakly reversible chemical reaction networks, for which a positive solution to ODEs cannot be proved to converge to an equilibrium point based on the DZT since one of the conditions, weak reversibility, is not satisfied. In order to make up for the failure of this important condition, by decomposing the network into weakly reversible sub-networks and applying DZT to them, we show any solution with positive initial values converges to an equilibrium point on the boundary of the positive orthant.