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

The initiation of reaction-diffusion travelling waves in two regions c oupled together by the linear diffusive interchange of an autocatalyti c species is considered. In one region a purely autocatalytic producti on 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 whic h travelling wave formation is possible as well as identifying two spe cial cases which need further consideration, namely cubic autocatalysi s in both regions with quadratic or linear decay in one region. The fo rmer case gives rise to a zero eigenvalue and the perturbation method has to be extended to include the higher order terms to resolve this c ase. The latter case requires a threshold on the initial input of auto catalyst and further information about this threshold is gained from a solution for strong coupling.