Limit cycles in the presence of convection, a travelling wave analysis

Abstract

We consider a diffusion model with limit cycle reaction functions, in the presence of convection. We select a set of functions derived from a realistic reaction model: the Schnakenberg equations. This resultant form is unsymmetrical. We find a transformation which maps the irregular equations into model form. Next we transform the dependent variables into polar form. From here, a travelling wave analysis is performed on the radial variable. Results are complex, but we make some simple estimates. We carry out numerical experiments to test our analysis. An initial `knock' starts the propagation of pattern. The speed of the travelling wave is not quite as expected. We investigate further. The system demonstrates distinctly different behaviour to the left and the right. We explain how this phenomenon occurs by examining the underlying behaviour.

arXiv comment20 pages, 5 figures

References in corpus (1)

• Stability of Moving Fronts in the Ginzburg-Landau Equation

Cited by in corpus (3)

• Principal bifurcations and symmetries in the emergence of reaction-diffusion-advection patterns on finite domains
• Towards nonlinear selection of reaction-diffusion patterns in presence of advection: A spatial dynamics approach
• Catalytic membrane reactor model as a laboratory for pattern emergence in reaction-diffusion-advection media