Multistability, oscillations and travelling waves in a product-feedback autocatalator model. II The initiation and propagation of travelling waves

Abstract

The initiation and propagation of reaction diffusion travelling waves in a model product-feedback autocatalator kinetic scheme, for which the well-stirred (spatially homogeneous) case has been considered previously in detail, in discussed. A priori bounds and general properties are obtained for the initial-value problem. These are extended by numerical solutions of the initial-value problem in the three, previously identified expanding, contracting and reduced cases. In the reduced case, the concentrations attained at the rear of the wave are seen to depend on the existence and temporal stability of a non-trivial steady state of the system. In the contracting case, a constant non-zero value is achieved by the concentration of reactant A, while the concentrations 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 permanent form travelling wave equations are then treated. General properties of their solutions are obtained and asymptotic solutions, valid for large initial concentrations of reactant A, are derived in all three cases.