Asymptotic stability of delayed complex balanced reaction networks with non-mass action kinetics

TL;DR

This paper proves that delayed complex balanced reaction networks with generalized kinetics have unique, locally asymptotically stable positive equilibria within each stoichiometric class, using Lyapunov methods.

Contribution

It extends stability results to delayed reaction networks with non-mass action kinetics using Lyapunov-Krasovskii functionals.

Findings

Unique positive equilibrium in each class is locally asymptotically stable.

Lyapunov-Krasovskii functional effectively proves stability in delayed systems.

Results demonstrated through illustrative examples.

Abstract

We consider delayed chemical reaction networks with generalized kinetics of product form 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.