Control and bifurcation theoretic analysis of gas-evolution oscillators

Abstract

Models that describe the dynamics of chemical oscillators are often associated with delayed feedback. In this paper, we focus on one such model proposed by Bar-Eli and Noyes to explain the mechanism of gas-evolution oscillators. First, a local stability analysis of the system is performed to obtain the necessary and sufficient condition for stability. It is identified that the loss of stability occurs through a Hopf bifurcation. A measure for the rate of convergence of the system to its steady state is found using the Lambert W function. Further, the orbital stability of the bifurcating periodic solutions and the type of Hopf bifurcation is analysed. Finally, we perform a robust stability analysis of the linearised system using Vinnicombe gap metric for parametric uncertainties. This control and bifurcation theoretic analysis aims to improve the mathematical understanding of the behaviour of gas-evolution oscillators.