Excitability, Wave Reflection, and Wave Splitting in a Cubic Autocatalysis Reaction-Diffusion System

The excitability properties of a two-variable cubic autocatalysis model for chemical oscillations are examined. The reaction-diffusion behaviour of this model is studied in a one-dimensional configuration with differing relative diffusivities of the species. Wave reflection at no-flux boundaries is examined and described in terms of reactant depletion in the wave front and reactant influx in the wave back. Waves are also reflected upon collision with other waves. Wave splitting, the spontaneous initiation of a wave from the trailing edge of another wave, is found to occur for some relative diffusivities. Successive wave splittings give rise to stationary Turing patterns at long times.