MULTISTABILITY, OSCILLATIONS AND TRAVELING WAVES IN A PRODUCT-FEEDBACK AUTOCATALATOR MODEL .2. THE INITIATION AND PROPAGATION OF TRAVELING WAVES

The initiation and propagation of reaction diffusion travelling waves in a model product-feedback autocatalator kinetic scheme, for which th e well-stirred (spatially homogeneous) case has been considered previo usly in detail, in discussed. A priori bounds and general properties a re obtained for the initial-value problem. These are extended by numer ical solutions of the initial-value problem in the three, previously i dentified expanding, contracting and reduced cases. In the reduced cas e, the concentrations attained at the rear of the wave are seen to dep end on the existence and temporal stability of a non-trivial steady st ate of the system. In the contracting case, a constant non-zero value is achieved by the concentration of reactant A, while the concentratio ns of autocatalyst B and reactant C are pulse-like and tend to zero at long times. In the expanding case, a propagating wave front is seen, but now the concentrations behind the wave can grow in time. The perma nent form travelling wave equations are then treated. General properti es of their solutions are obtained and asymptotic solutions, valid for large initial concentrations of reactant A, are derived in all three cases.