Abstract
The Deficiency Zero Theorem (DZT) is extended to be applied to chemical reaction networks (CRNs) with time delays, the time evolution of concentrations of species in which networks is described by delay differential equations (DDEs). The extended DZT provides a sufficient condition for a positive equilibrium point of DDEs to exist and be locally asymptotically stable. Furthermore, it is proven that the absence of boundary equilibria is a sufficient condition for the positive equilibrium point to be globally asymptotically stable. These results are natural analogues of theorems proven for CRNs without time delays.
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