Asymptotic Stability of Delayed Complex Balanced Reaction Networks with Non-Mass Action Kinetics

We consider delayed chemical reaction networks with non-mass action monotone kinetics and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is locally asymptotically stable relative to its class. The main tools of the proofs are respectively a version of the well-known classical logarithmic Lyapunov function applied to kinetic systems and its generalization to the delayed case as a Lyapunov–Krasovskii functional. Finally, we demonstrate our results through illustrative examples.