The Development of Travelling Waves in a Simple Isothermal Chemical System with General Orders of Autocatalysis and Decay

We examine the possibility of generating a propagating chemical wave front when a local input of an autocatalyst B is introduced into a uniform concentration of a reactant A. The autocatalysis is assumed to be of order m, so that A --> B at a rate k₁ [A][B]^m, while the autocatalyst decays to an inert product C at a rate of order n, B --> C, rate k₂[B]ⁿ. The situation is examined for m, n >= 1 and emphasis placed on obtaining threshold criteria for the development of reaction-diffusion fronts.