Patterns of a General Chemical Model Involving Degn-Harrison Reaction Scheme

Abstract

This paper reports the pattern formation of a general Degn-Harrison system. We first determine the types and stability of the unique positive equilibrium for the spatially homogeneous system. The equilibrium may be node, focus, or center. Supercritical or subcritical Hopf bifurcation may occur if it is a center. In the sequel, we propose the conditions for the occurrence of Turing instability for the spatially inhomogeneous system. We can theoretically explain that Turing instability exists as the equilibrium transitions from homogeneous stable to inhomogeneous unstable states. Finally, we perform computational experiments to investigate the complex pattern formation of this chemical model. An interesting finding is that if one of the reactants has a high diffusion rate, the pattern formation will be inhibited. Conversely, a low diffusion rate may promote pattern formation.