On Stability of Two Kinds of Delayed Chemical Reaction Networks

TL;DR

This paper investigates the stability of two classes of delayed chemical reaction networks, proving stability for one class and defining conditions for stability in a special subclass of the other.

Contribution

It establishes the existence of a class of delayed networks that remain conjugate to complex balanced systems and analyzes their stability properties.

Findings

Proves local asymptotic stability for the first class of networks.

Defines a subclass of the second class and proves its stability.

Provides examples illustrating the theoretical results.

Abstract

For the networks that are linear conjugate to complex balanced systems, the delayed version may include two classes of networks: one class is still linear conjugate to the delayed complex balanced network, the other is not. In this paper, we prove the existence of the first class of networks, and emphasize the local asymptotic stability relative to a certain defined invariant set. For the second class of systems, we define a special subclass and derive the local asymptotic stability for the subclass. Two examples are provided to illustrate our results.