THE EFFECTS OF COUPLING ON CHEMICAL WAVE-PROPAGATION IN QUADRATIC AND CUBIC AUTOCATALYSIS WITH DECAY

The initiation of reaction-diffusion travelling waves in two regions coupled together by the linear diffusive interchange of an autocatalytic species is considered. In one region a purely autocatalytic production process (either quadratic or cubic) is assumed, while in the other region there are both autocatalytic and decay processes (either linear or quadratic). A perturbation analysis based on small initial inputs of the autocatalyst is presented. This indicates conditions under which travelling wave formation is possible as well as identifying two special cases which need further consideration, namely cubic autocatalysis in both regions with quadratic or linear decay in one region. The former case gives rise to a zero eigenvalue and the perturbation method has to be extended to include the higher order terms to resolve this case. The latter case requires a threshold on the initial input of autocatalyst and further information about this threshold is gained from a solution for strong coupling.