Dissipative Structures in 1D and 2D Chemically Reacting Systems

Abstract

Abstract A transient analysis of the 1D and 2D reaction-diffusion equations associated with the model reaction of Prigogine and Lefever (Brusselator model), including diffusion of the initial (sub-strate) component, has been performed. For low system lengths and for fixed boundary conditions, the steady state low amplitude solutions are unstable. For zero flux boundary conditions a multiplicity of symmetric solutions with the same wave number may exist, the majority of them being unstable. The diffuion of initial components induce relaxation oscillations in space both for fixed as well as zero flux boundary conditions. The amplitude of the oscillation increases as the diffusion coefficient of the initial component decreases. For conditions of relaxation oscillations the spatial profiles result in single or multiple propagating fronts. High system lengths (or low diffusion coefficient of intermediate components), for both zero flux and periodic boundary conditions, may give rise to a multipeak incoherent wave pattern. For periodic boundary conditions a multiplicity of waves has been observed. Numerical simulation of the 2D-spatial structures reveal certain similarities between the 1D and 2D cases.