Stability analysis for single linkage class chemical reaction networks with distributed time delays⋆

Abstract

In the present paper, we show two results concerning stability for a class of single linkage class chemical reaction networks (CRNs) with distributed time delays, all complexes of which are distinct. The dynamics of concentrations of species of the CRN with mass action kinetics (MAK) are described by the functional differential equations (FDEs) with distributed time delays for each reaction. As the first result, we show that any positive solution to the FDE of weakly reversible CRN globally converges to a positive equilibrium point in the functional state space. As the second result, we prove that any positive solution to the FDE of non-weakly reversible CRNs globally converges to a non-negative equilibrium point on the boundary of the positive orthant by decomposing the whole network into weakly reversible subnetworks and analyzing the stability of each subnetwork.