On global stability of the Lotka reactions with generalized mass-action kinetics

TL;DR

This paper investigates the global stability of the positive equilibrium in Lotka reactions with generalized mass-action kinetics, providing conditions based on kinetic orders for stability in power-law dynamical systems.

Contribution

It characterizes the global asymptotic stability of the equilibrium in Lotka reactions with arbitrary power-law kinetics, extending classical results.

Findings

Conditions for existence and uniqueness of positive equilibrium

Criteria for global asymptotic stability based on kinetic orders

Analysis of power-law dynamical systems in chemical reactions

Abstract

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particular, we characterize its global asymptotic stability in terms of the kinetic orders.