Local phase and renormalized frequency in inhomogeneous chemioscillations

Abstract

Inhomogeneous evolution of a chemically reacting system capable of a homogeneous oscillation is analyzed in terms of a nonsecular perturbation method. This ’’phase diffusion’’ theory takes account of the local phase shifts and frequency renormalization that occurs due to the interaction of reaction and diffusion. The theory is used to show that oscillator like plane waves are stable to small perturbations. Boundary value problems including those for a finite volume impermeable vessel, a ring shaped vessel (periodic boundary condition) and catalytic walls and membranes are shown to lead to stable oscillatory states some of which are inhomogeneous for all times. The structure of the theory allows for clear qualitative interpretations. Several experiments are suggested for the purpose of verification of the theory and the phenomena predicted.